The areal velocity of mars around the sun does not change while it revolves around the sun, according to Kepler's law. As a result, the areal velocity versus time graph is a straight line.
Draw areal velocity versus time graph for mars.
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Physics
The centre of mass of an extended body on the surface of the earth and its centre of gravity
a) are always at the same point for any size of the body
b) are always at the same point only for spherical bodies
c) can never be at the same point
d) is close to each other for objects, say of sizes less than 100 m
e) both can change if the object is taken deep inside the earth
The correct option is d) is close to each other for objects, say of sizes less than 100 m
Which of the following are true?
a) a polar satellite goes around the earth’s pole in a north-south direction
b) a geostationary satellite goes around the earth in an east-west direction
c) a geostationary satellite goes around the earth in a west-east direction
d) a polar satellite goes around the earth in an east-west direction
The correct options are a) a polar satellite goes around the earth’s pole in a north-south direction c) a geostationary satellite goes around the earth in a west-east direction
Which of the following options is correct?
a) acceleration due to gravity decreases with increasing altitude
b) acceleration due to gravity increases with increasing depth
c) acceleration due to gravity increases with increasing latitude
d) acceleration due to gravity is independent of the mass of the earth
The correct options are a) acceleration due to gravity decreases with increasing altitude c) acceleration due to gravity increases with increasing latitude
The initial state of a certain gas is Pi, Vi, Ti. It undergoes expansion till its volume becomes Vf. Consider the following two cases:
a) the expansion takes place at constant temperature b) the expansion takes place at constant pressure Plot the P-V diagram for each case. In which of the two cases, is the work done by the gas...
If the coefficient of performance of a refrigerator is 5 and operates at the room temperature, find the temperature inside the refrigerator.
Answer: To determine the temperature inside the refrigerator, we must first determine the work that has been done. W = 0 Q1 = Q2 β = ∞ Where β represents the coefficient of performance According to...
In a refrigerator, one removes heat from a lower temperature and deposits to the surroundings at a higher temperature. In this process, mechanical work has to be done, which is provided by an electric motor. If the motor is of 1kW power, and heat is transferred from -3oC to 27oC, find the heat taken out of the refrigerator per second assuming its efficiency is 50% of a perfect engine.
Answer: Expression for the efficiency of the Carnot engine is as follows; $ \eta =1-\frac{{{T}_{2}}}{{{T}_{1}}} $ Where T1 = 300 K and T2 = 270 K We are given that the efficiency is 50% = 0.5...
Consider a cycle tyre being filled with air by a pump. Let V be the volume of the tyre and at each stroke of the pump ∆V of air is transferred to the tube adiabatically. What is the work done when the pressure in the tube is increased from P1 to P2?
Answer: The equation before and after the stroke can be written as follows: $ {{P}_{1}}{{V}_{1}}={{P}_{2}}V_{2}^{\gamma } $ $ P{{\left( V+\Delta V \right)}^{\gamma }}=(P+\Delta P){{V}^{\gamma }} $ $...
A person of mass 60 kg wants to lose 5 kg by going up and down a 10 m high stairs. Assume he burns twice as much fat while going up than coming down. If 1 kg of fat is burnt on expending 7000 kilocalories, how many times must he go up and down to reduce his weight by 5 kg?
Answer: According to the question, the height of the stairs is h = 10 m And the work done to burn 5 kg of fat is W = (5)(7000 × 103)(4.2) W = 147 × 106 J Therefore, the work done towards burning of...
Consider a Carnot’s cycle operating between T1 = 500K and T2 = 300K producing 1 kJ of mechanical work per cycle. Find the heat transferred to the engine by the reservoirs.
Answer: According to the question, the temperature of the source is T1 = 500 K and the temperature of the sink is T2 = 300 K We also have the work done per cycle as W = 1 kJ = 1000 J we have to...
Air pressure in a car tyre increases during driving. Explain.
Answer: According to Charle's law, the air pressure in a car tyre increases while the volume remains constant during driving. Temperature and pressure are proportional. As a result, the pressure of...
Is it possible to increase the temperature of a gas without adding heat to it? Explain.
Yes, it is possible to raise a gas's temperature without adding heat to it. During adiabatic compression, this is feasible. In adiabatic compression, we know that dQ=0 ∴ Making use of the first law...
If a refrigerator’s door is kept open, will the room becomes cool or hot? Explain.
Answer: When a refrigerator door is left open, the room becomes hot because the quantity of heat received by the refrigerator, as well as the work performed by the refrigerator, is rejected into the...
A system goes from P to Q by two different paths in the P-V diagram as shown in the figure. Heat given to the system in the path 1 is 1000 J. The work done by the system along path 1 is more than path 2 by 100 J. What is the heat exchanged by the system in path 2?
Answer: From path 1 we can say that, Q1 = +1000 J and the work done is W1 – W2 = 100 Where W1 represents the work done through path 1 and W2 denotes the work done through path 2. Therefore, we can...
Can a system be heated and its temperature remains constant?
Answer: Yes, if the complete amount of heat provided to the system is used for expansion. To maintain a constant temperature, the system's work against the environment should be compensated by the...
Consider a heat engine as shown on the figure. Q1 and Q2 are heat added to heat bath T1 and heat taken from T2 in one cycle of the engine. W is the mechanical work done on the engine.
If W > 0, then possibilities are: a) Q1 > Q2 > 0 b) Q2 > Q1 > 0 c) Q2 < Q1 < 0 d) Q1 < 0, Q2 > 0 Answer: The correct options are a) Q1 > Q2 > 0 c) Q2 < Q1 < 0...
Consider a cycle followed by an engine
1 to 2 is isothermal 2 to 3 is adiabatic 3 to 1 is adiabatic Such a process does not exist because a) heat is completely converted to mechanical energy in such a process, which is not possible b)...
Figure shows the P-V diagram of an ideal gas undergoing a change of state from A to B. Four different parts I, II, III, and IV as shown in the figure may lead to the same changes of state.
a) change in internal energy is the same in IV and III cases, but not in I and II b) change in internal energy same in all the four cases c) work done is maximum in case I d) work done is minimum in...
An ideal gas undergoes isothermal process from some initial state I to final state f. Choose the correct alternatives
a) dU = 0 b) dQ = 0 c) dQ = dU d) dQ = dW Answer: The correct options are a) dU = 0 d) dQ = dW Explanation: Internal energy is a function of temperature. Since temperature is constant...
Which of the process described below are irreversible?
a) the increase in temperature of an iron rod by hammering it b) a gas in a small container at a temperature T1 is brought in contact with a big reservoir at a higher temperature T2 which increases...
Three copper blocks of masses M1, M2, and M3 kg respectively are brought into thermal contact till they reach equilibrium. Before contact, they were at T1, T2, T3 (T1 > T2 > T3). Assuming there is no heat loss to the surroundings, the equilibrium temperature T is
a) b) c) d) Answer: The correct option is b)
Consider two containers A and B containing identical gases at the same pressure, volume, and temperature. The gas in container A is compressed to half of its volume isothermally while the gas in the container B is compressed to half of its original value adiabatically. The ratio of final pressure of a gas in B to that of gas in A is
Answer: The correct answer is a)
An ideal gas undergoes cyclic process ABCDA as shown in the given P-V diagram. The amount of work done by the gas is
a) 6P0V0 b) -2P0V0 c) +2P0V0 d) +4P0V0 Answer: The correct option is d) +4P0V0 Explanation Work done by the gas is equal to the area of rectangle ABCDA =AB×BC =(2V0)P0 =2P0V0 This work is done on...
Consider P-V diagram for an ideal gas shown in the figure.
Out of the following diagrams, which represent the T-P diagram? a) iv b) ii c) iii d) i Answer: The correct option is c) iii Explanation: In the above-mentioned graph, PV=constant Moreover, PV=nRT...
If an average person jogs, he produces 14.5 × 103 cal/min. This is removed by the evaporation of sweat. The amount of sweat evaporated per minute is assuming 1 kg requires 580 × 103 cal for evaporation
a) 0.25 kg b) 2.25 kg c) 0.05 kg d) 0.20 kg Answer: The correct option is a) 0.25 kg Explanation: Energy produces = 14.5 × 103 cal/min. Then the amount of sweat evaporated per min is given...
An ideal gas undergoes four different processes from the same initial state. Four processes are adiabatic, isothermal, isobaric, and isochoric. Out of 1, 2, 3, and 4 which one is
a) 4 b) 3 c) 2 d) 1 Answer: The correct option is c) 2 Explanation: The adiabatic process occurs when a thermodynamic system changes in such a way that no heat exchange occurs between it and its...
According to Stefan’s law of radiation, a black body radiates energy σT4 from its unit surface area every second where T is the surface temperature of the black body and σ = 5.67 × 10-8 W/m2K4 is known as Stefan’s constant. A nuclear weapon may be thought of as a ball of radius 0.5 m. When denoted, it reaches temperature of 106K and can be treated as a black body.
c) if all this energy U is in the form of radiation, corresponding momentum is p = U/c. How much momentum per unit time does it impart on unit area at a distance of 1 km? Answer: (c) According to...
According to Stefan’s law of radiation, a black body radiates energy σT4 from its unit surface area every second where T is the surface temperature of the black body and σ = 5.67 × 10-8 W/m2K4 is known as Stefan’s constant. A nuclear weapon may be thought of as a ball of radius 0.5 m. When denoted, it reaches temperature of 106K and can be treated as a black body.
a) estimate the power it radiates b) if surrounding has water at 30oC, how much water can 10% of the energy produced evaporate in 1 sec? Answer: a) We know that the expression for the power radiated...
A thin rod having length Lo at 0 degrees C and coefficient of linear expansion α has its two ends maintained at temperatures θ1 and θ2, respectively. Find its new length. Answer: Consider the following diagram
Answer: Consider the following diagram: From the diagram, this much can be said that: $ \theta =\frac{{{\theta }_{1}}+{{\theta }_{2}}}{2} $ The temperature changes in a linear fashion from θ1 to...
A rail track made of steel having length 10 m is clamped on a railway line at its two ends. On a summer day due to rise in temperature by 20oC, it is deformed as shown in the figure. Find x if αsteel = 1.2 × 10-5/oC.
Answer: According to the question, we have - αsteel = 1.2 × 10-5/oC and Lo = 10 m ∆T = 20oC Making use of the Pythagoras theorem, we have; $ {{x}^{2}}={{\left[ \frac{1}{2}(L+\Delta L)...
Calculate the stress developed inside a tooth cavity filled with copper when hot tea at a temperature of 57oC is drunk. You can take body temperature to be 37oC and α = 1.7 × 10-5oC, bulk modulus for copper = 140 × 109 N/m2.
Answer: According to the question, decrease in temperature is as follows: ∆t = 57 – 37 = 20oC The coefficient of linear expansion is as follows: α = 1.7 × 10-5oC And the bulk modulus for copper is:...
We would like to make a vessel whose volume does not change with temperature. We can use brass and iron (βbrass = 6 × 10-6/K and βiron = 3.55 × 10-5/K) to create a volume of 100 cc. How do you think you can achieve this?
Answer: According to the question, the volume of vessel is V = 100 cm3 = 10-4 = constant We also have that the volume of the iron vessel – Volume of brass rod = 10-4 m3 We know that: $ {{\beta...
We would like to prepare a scale whose length does not change with temperature. It is proposed to prepare a unit scale of this type whose length remains, say 10 cm. We can use a bimetallic strip made of brass and iron each of different length whose length would change in such a way that difference between their lengths remain constant. If αiron = 1.2 × 10-5/K and αbrass = 1.8 × 10-5/K, what should we take as length of each strip?
Answer: Change in length of iron rod is given as follows: $ \Delta L={{\alpha }_{iron}}{{L}_{iron}}\Delta T $ Change in length of brass rod is given as follows: $ \Delta L={{\alpha...
One day in the morning, Ramesh filled up 1/3 bucket of hot water from geyser, to take bath. Remaining 2/3 was to be filled by cold water to bring mixture to a comfortable temperature. Suddenly Ramesh had to attend something which would take some times, say 5-10 minutes before he could take bath. Now he has two options:
a) fill the remaining bucket completely by cold water and then attend the work b) first attend to the work and fill the remaining bucket just before taking bath. Which option do you think would have...
100 g of water is supercooled to -10 degrees C. At this point, due to some disturbance mechanised or otherwise some of it suddenly freezes to ice. What will be the temperature of the resultant mixture and how much mass would freeze?
Answer: According to the question, the mass of water is 100 g At -10 degrees Celsius, the mixture has water and ice The expression for the heat required by the mixture is as follows: ms∆t =...
During summers in India, one of the common practice to keep cool is to make ice balls of crushed ice, dip it in flavoured sugar syrup and sip it. For this a stick is inserted into crushed ice and is squeezed in the palm to make it into the ball. Equivalently in winter, in those areas where it snows, people make snow balls and throw around. Explain the formation of ball out of crushed ice or snow in the light P-T diagram of water.
Answer: The graph above depicts the relationship between water pressure and temperature. When the pressure is increased, the ice becomes liquid, and when the pressure is decreased, it becomes solid....
Find out the increase in moment of inertia I of a uniform rod about its perpendicular bisector when its temperature is slightly increased by ∆T.
Answer: The picture above depicts a rod with a uniform mass M and a length l that is bisected perpendicularly. $ I=\frac{1}{12}M{{l}^{2}} $ When the temperature is raised, the rod length increases...
These days people use steel utensils with copper bottom. This is supposed to be good for uniform heating of food. Explain this effect using the fact that copper is the better conductor.
Answer: Copper bottom utensils are utilised because, when compared to steel, copper is a better heat conductor. As a result, copper-bottomed utensils are utilised, and heat is distributed evenly....
Calculate the temperature which has same numerical value on Celsius and Fahrenheit scale.
Answer: For the construction of the temperature scale, consider two fixed points. The lower fixed point is the initial fixed point, which is for the freezing point. The upper fixed point is the...
Why does a metal bar appear hotter than a wooden bar at the same temperature? Equivalently it also appears cooler than wooden bar if they are both colder than room temperature.
Answer: Because the rate of heat transfer through metal is faster than in wood, a metal bar seems to be hotter than a hardwood bar at the same temperature. Similarly, a metal bar appears to be...
A student records the initial length l, change in temperature ∆T and change in length ∆l of a rod as follows:
Sl.no l (m) ∆T (oC) ∆l (m) 1 2 10 4 × 10-4 2 1 10 4 × 10-4 3 2 20 2 × 10-4 4 3 10 6 × 10-4 If the first observation is correct, what can you say about observations 2, 3, and 4. Answer: Assume that...
The centre of gravity of a body on the earth coincides with its centre of mass for a ‘small’ object whereas for an ‘extended’ object it may not. What is the qualitative meaning of ‘small’ and ‘extended’ in this regard? For which of the following the two coincides? A building, a pond, a lake, a mountain?
The geometric centre of gravity is the geometric centre, but the mass of the place where the complete mass of the body is considered is the mass of the centre of mass. When an object's vertical...
Is the bulb of a thermometer made of diathermic or adiabatic wall?
Answer: A thermometer's bulb is made of diathermic walls, which allow heat to pass through. The bulb of a thermometer is built of diathermic walls, which enable heat energy to be exchanged between...
A glass full of hot milk is poured on the table. It begins to cool gradually. Which of the following is correct?
a) the rate of cooling is constant till milk attains the temperature of the surrounding b) the temperature of milk falls off exponentially with time c) while cooling, there is a flow of heat from...
Refer to the plot of temperature versus time showing the changes in the state of ice on heating. Which of the following is correct?
a) the region AB represents ice and water in thermal equilibrium b) at B water starts boiling c) at C all the water gets converted into steam d) C to D represents water and steam in equilibrium at...
‘Gulab Jamuns’ (assumed to be spherical) are to be heated in an oven. They are available in two sizes, one twice bigger than the other. Pizzas (assumed to be discs) are also to be heated in the oven. They are also in two sizes, one twice big in radius than the other. All four are put together to be heated to oven temperature. Choose the correct option from the following:
a) both size gulab jamuns will get heated at the same time b) smaller gulab jamuns are heated before bigger ones c) smaller pizzas are heated before bigger ones d) bigger pizzas are heated before...
Mark the correct options:
a) A system X is in thermal equilibrium with Y but not with Z. System Y and Z may be in thermal equilibrium with each other b) A system X is in thermal equilibrium with Y but not with Z. Systems Y...
A sphere, a cube, and a thin circular plate, all of the same material and same mass are initially heated to same high temperature.
a) plate will cool fastest and cube the slowest b) sphere will cool fastest and cube the slowest c) plate will cool fastest and sphere the slowest d) cube will cool fastest and plate the slowest...
The radius of a metal sphere at room temperature T is R, and the coefficient of linear expansion of the metal is α. The sphere is heated a little by a temperature ∆T so that its new Temperature is T + ∆T. The increase in the volume of the sphere is approximately
Answer: The correct option is d).
Heat is associated with
a) kinetic energy of random motion of molecules b) kinetic energy of orderly motion of molecules c) total kinetic energy of random and orderly motion of molecules d) kinetic energy of random motion...
As the temperature is increased, the time period of a pendulum
a) increases as its effective length increases even though its centre of mass still remains at the centre of the bob b) decreases as its effective length increases even though its centre of mass...
An aluminium sphere is dipped into water. Which of the following is true?
a) buoyancy will be less in water at 0oC than that in water at 4oC b) buoyancy will be more in the water at 0oC than that in water at 4oC c) buoyancy in water at 0oC will be same as that in the...
The graph between two temperature scales A and B is shown in the figure. Between upper fixed point and the lower fixed point, there are 150 equal division on scale A and 100 on scale B. The relationship for conversion between the two scales is given by
Answer: The correct answer is b)
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly
a) its speed of rotation increases b) its speed of rotation decreases c) its speed of rotation remains the same d) its speed increases because its moment of inertia increases Answer: The correct...
A bimetallic strip is made of aluminium and steel (αAl > αsteel). On heating, the strip will
a) remain straight b) get twisted c) will bend with aluminium on the concave side d) will bend with steel on the concave side Answer: The correct option is d) will bend with steel on the concave...
In a shotput event an athlete throws the shotput of mass 10 kg with an initial speed of 1 m/s at 45o from height 1.5 m above ground. Assuming air resistance to be negligible and acceleration due to gravity to be 10 m/s2, the kinetic energy of the shotput when it just reaches the ground will be a) 2.5 J b) 5.0 J c) 52.5 J d) 155.0 J
d) 155.0 J
A mass of 5 kg is moving along a circular path of radius 1 m. If the mass moves with 300 revolutions per minute, its kinetic energy would be a) 250π2 b) 100 π2 c) 5 π2 d) 0
a) 250π2
Which of the diagrams shown in the figure represents variations of total mechanical energy of a pendulum oscillating in air as a function of time?
c)
Which of the diagrams shown in figure most closely shows the variation in kinetic energy of the earth as it moves once around the sun in its elliptical orbit?
d)
A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in the figure correctly shows the displacement-time curve for its motion?
b)
A body of mass 0.5 kg travels in a straight line with velocity v = ax3/2 where a = 5 m-1/2s-1. The work done by the net force during its displacement from x = 0 to x = 2 m is a) 1.5 J b) 50 J c) 10 J d) 100 J
b) 50 J
The potential energy function for a particle executing linear SHM is given by where k is the force constant of the oscillator. For k = 0.5 N/m, the graph of V(x) versus x is shown in the figure. A particle of total energy E turns back when it reaches x = ±xm, then which of the following is correct?a) V = O, K = E b) V = E, K = O c) V < E, K = O d) V = O, K < E
b) V = E, K = O
Two inclined frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track as shown in the figure. Which of the following statement is correct?a) both the stones reach the bottom at the same time but not with the same speed b) both stone reach the bottom with the same speed and stone I reaches the bottom earlier than stone II c) both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I d) both the stones reach the bottom at different times and with different speeds
c) both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I
During inelastic collision between two bodies, which of the following quantities always remain conserved? a) total kinetic energy b) total mechanical energy c) total linear momentum d) speed of each body
c) total linear momentum
A body is falling freely under the action of gravity alone in a vacuum. Which of the following quantities remain constant during the fall? a) kinetic energy b) potential energy c) total mechanical energy d) total linear momentum
c) total mechanical energy
A bicyclist comes to a skidding stop in 10 m. During this process, the force on the bicyclist due to the road is 200 N and is directly opposed to the motion. The work done by the cycle on the road is a) +2000 J b) -200 J c) zero d) -20,000 J
c) zero
A man squatting on the ground gets straight up and stand. The force of reaction of ground on the man during the process is a) constant and equal to mg in magnitude b) constant and greater than mg in magnitude c) variable but always greater than mg d) at first greater than mg, and later becomes equal to mg
d) at first greater than mg, and later becomes equal to mg
A proton is kept at rest. A positively charged particle is released from rest at a distance d in its field. Consider two experiments; one in which the charged particles is also a proton and in another, a positron. In the same time t, the work done on the two moving charged particles is a) the same as the same force law is involved in the two experiments b) less for the case of a positron, as the positron moves away more rapidly and the force on it weakens c) more for the case of a positron, as the positron moves away from a larger distance d) same as the work done by charged particle on the stationary proton
c) more for the case of a positron, as the positron moves away from a larger distance
An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. This is because, a) the two magnetic forces are equal and opposite, so they produce no net effect b) the magnetic forces do no work on each particle c) the magnetic forces do equal and opposite work on each particle d) the magnetic forces are necessarily negligible
b) the magnetic forces do no work on each particle
A merry-go-round, made of a ring-like platform of radius R and mass M, is revolving with angular speed ω. A person of mass M is standing on it. At one instant, the person jumps off the ground, radially away from the centre of the round. The speed of the round afterwards is
a) 2ω
b) ω
c) ω/2
d) 0
Correct answer is a) 2ω
A hot air balloon is a sphere of radius 8 m. The sir inside is at a temperature of 60oC. How large a mass can the balloon lift when the outside temperature is 20oC?
Answer: Suppose that pi represents the pressure inside the balloon and po represents the pressure outside the balloon. Then the excess pressure can be written as: pi – po = 2T/r Where, T represents...
Surface tension is exhibited by liquids due to the force of attraction between molecules of the liquid. The surface tension decreases with increase in temperature and vanishes at boiling point. Give that the latent heat of vaporisation for water Lv = 540 k cal/kg, the mechanical equivalent of heat J = 4.2 J/cal, density of water ρw = 103 kg/l, Avogadro’s number NA = 6.0 1026 k/mole, and the molecular weight of water MA = 18 kg for 1 k mole.
c) 1 g of water in the vapour state at 1 atm occupies 1601 cm3. Estimate the intermolecular distance at boiling point, in the vapour state. d) During vaporisation a molecule overcomes a force F,...
surface tension is exhibited by liquids due to the force of attraction between molecules of the liquid. The surface tension decreases with increase in temperature and vanishes at boiling point. Give that the latent heat of vaporisation for water Lv = 540 k cal/kg, the mechanical equivalent of heat J = 4.2 J/cal, density of water ρw = 103 kg/l, Avogadro’s number NA = 6.0 1026 k/mole, and the molecular weight of water MA = 18 kg for 1 k mole.
a) Estimate the energy required for one molecule of water to evaporate. b) Show that the inter-molecular distance for water is Answer : a) According to the question, the latent heat of vaporization...
c) If po = 1.03 × 105 N/m2, ρo = 1.29 kg/m3 and g is 9.8 m/s2 at what height will the pressure drop to (1/10) the value at the surface of the earth? d) This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.
Answer: (c) We know that - $ p={{p}_{0}}{{e}^{\left( -\frac{{{\rho }_{0}}gh}{{{p}_{0}}} \right)}} $ By substituting the known values, we can determine that h = 18.43 km (d) For $ \rho \alpha p $ to...
a) Pressure decreases as one ascends the atmosphere. If the density of air is ρ, what is the change in pressure dp over a differential height dh? b) Considering the pressure p to be proportional to the density, find the pressure p at a height h if the pressure on the surface of the earth is ρo.
Answer: (a) The pressure falls as we ascend higher because the thickness of the gas above us diminishes. Let A be the cross-section of the air's horizontal layer, and dh be its height. The pressure...
The surface tension and vapour pressure of water at 20oC is 7.28 × 10-2 N/m and 2.33 × 103 Pa, respectively. What is the radius of the smallest spherical water droplet which can form without evaporating at 20oC?
Answer: According to the question, the surface tension of water is T = 7.28 × 10-2 N/m and the vapour pressure is P = 2.33 × 103 Pa Let r represent the radius of the drop The excess pressure that is...
If a drop of liquid breaks into smaller droplets, it results in lowering of the temperature of the droplets. Let a drop of radius R, break into N small droplets each of radius r. Estimate the drop in temperature.
Answer: The volume of a drop of liquid with a radius of R = (N) (volume of a liquid droplet of radius r) $ \frac{4}{3}\pi {{R}^{3}}=N\times \frac{4}{3}\pi {{r}^{3}} $ $ N=\frac{{{R}^{3}}}{{{r}^{3}}}...
Two mercury droplets of radii 0.1 cm and 0.2 cm collapse into one single drop. What amount of energy is released? The surface tension of mercury T = 435.5 × 10-3 N/m.
Answer : The two drops should combine to make a larger drop in order to conserve volume. The radius of smaller drop is given as follows: r1 = 0.1 cm = 10-3 m Also, the radius of the bigger drop is...
The free surface of the oil in a tanker, at rest, is horizontal. If the tanker starts accelerating the free surface will be titled by an angle θ. If the acceleration is a m/s2, what will be the slope of the free surface?
Answer: Let m be the mass of an elementary oil particle. The balancing forces are angled in the surface's direction. Pseudo force is given by ma mg represents the height of a small part of the oil...
The sap in trees, which consists mainly of water in summer, rises in a system of capillaries of radius r = 2.5 × 10-5 m. The surface tension of sap is T = 7.28 × 10-2 N/m and the angle of contact is 0o. Does surface tension alone account for the supply of water to the top of all tress?
Answer: according to the question, the radius is r = 2.5 × 10-5 m The surface tension is T = 7.28 × 10-2 N/m It is also given that the angle of contact is θ = 0 degrees and the density is ρ = 103...
A cubical block of density ρ is floating on the surface of the water. Out of its height L, fraction x is submerged in water. The vessel is in an elevator accelerating upwards with acceleration a. What is the fraction immersed?
Answer : Let ρ represent the density of a block and let height of the block be L Then, we can write the expression for the mass of the block as follows: m = Vρ = L3ρ Then, the weight of the block is...
A cubical block of density ρ is floating on the surface of the water. Out of its height L, fraction x is submerged in water. The vessel is in an elevator accelerating upwards with acceleration a. What is the fraction immersed?
Answer : Let ρ represent the density of a block and let height of the block be L Then, we can write the expression for the mass of the block as follows: m = Vρ = L3ρ Then, the weight of the block is...
A vessel filled with water is kept on a weighing pan and the scale adjusted to zero. A block of mass M and density ρ is suspended by a massless spring of spring constant k. This block is submerged inside into the water in the vessel. What is the reading of the scale?
Answer: We know that the upthrust of the block is equal to the weight of water displaced. The expression of which can be written as follows Vρwg Let x represent the compression in the spring. So,...
An iceberg floats in water with part of it submerged. What is the fraction of the volume of an iceberg submerged if the density of ice is ρi = 0.917 g/cm3?
Answer: According to the question, the density of ice is ρice = 0.917 g/cm3 The density of water is ρwater = 1 g/cm3 Let Vi represent the volume of the iceberg and Vw denote the volume of the water...
Is surface tension a vector?
Answer: Surface tension is a scalar quantity as it has a specific direction. Surface tension is given by the expression : σ = W.D / Change in surface area As it is equal to the work done per unit...
Is viscosity a vector?
Answer: Viscosity is not a vector quantity. Viscosity is a liquid attribute that's equal to the amount of dragging force per unit area between two liquid layers with the same velocity gradient. As a...
Streamline flow is more likely for liquids with
a) high density b) high viscosity c) low density d) low viscosity Answer: The correct options are : b) high viscosity c) low density Explanation: Streamline flow is highly likely for liquids with...
With increase in temperature, the viscosity of
a) gases decreases b) liquids increases c) gases increases d) liquids decreases Answer: The correct options are : c) gases increases d) liquids decreases Explanation : Because the viscosity of...
A wooden block with a coin placed on its top, floats in water as shown in the figure:
The distance l and h are shown in the figure. After some time the coin falls into the water. Then a) l decreases b) h decreases c) l increases d) h increases Answer: The correct options are : a) l...
Pressure is a scalar quantity because
a) it is the ratio of force to the area and both force and area are vectors b) it is the ratio of the magnitude of the force to area c) it is the ratio of a component of the force normal to the area...
For a surface molecule
a) the net force on it is zero b) there is a net downward force c) the potential energy is less than that of a molecule inside d) the potential energy is more than that of a molecule inside Answer:...
The angle of contact at the interface of water-glass is 0o, ethyl alcohol-glass is 0o, mercury-glass is 140o, and methyl iodide-glass is 30o. A glass capillary is put in a trough containing one of these four liquids. It is observed that the meniscus is convex. The liquid in the trough is
a) water b) ethyl alcohol c) mercury d) methyl iodide Answer : The correct answer c) mercury If the contact angle is obtuse, the liquid meniscus in a capillary tube will be convex upwards. When one...
An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters 2.5 cm and 3.75 cm. The ratio of the velocities in the two pipes is
a) 9:4 b) 3:2 c) √3: √2 d) √2: √3 Answer: The correct answer a) 9:4 $ {{A}_{1}}{{v}_{1}}={{A}_{2}}{{v}_{2}} $ $ \frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{A}_{1}}}{{{A}_{2}}}={{\left(...
Along a streamline
a) the velocity of a fluid particle remains constant b) the velocity of all fluid particles crossing a given position is constant c) the velocity of all fluid particles at a given instant is...
Which of the following diagrams does not represent a streamline flow?
The correct answer is d) Lines of flow do not intersect each other.
A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in the figure, indicate the one that represents the velocity (v) of the pebble as a function of time (t).
Answer: The correct answer is c)
A stone of mass m is tied to an elastic string of negligible mass and spring constant k. The unstretched length of the string is L and has negligible mass. The other end of the string is fixed to a nail at a point P. Initially, the stone is at the same level as the point P. The stone is dropped vertically from point P.
c) what shall be the nature of the motion after the stone has reached its lowest point? Answer: After the stone has reached its lowest position, the motion becomes z0. It is given by the expression...
A stone of mass m is tied to an elastic string of negligible mass and spring constant k. The unstretched length of the string is L and has negligible mass. The other end of the string is fixed to a nail at a point P. Initially, the stone is at the same level as the point P. The stone is dropped vertically from point P.
a) find the distance y from the top when the mass comes to rest for an instant, for the first time b) what is the maximum velocity attained by the stone in this drop? According to the figure, PE of...
In nature, the failure of structural members usually result from large torque because of twisting or bending rather than due to tensile or compressive strains. This process of structural breakdown is called buckling and in cases of tall cylindrical structures like trees, the torque is caused by its own weight bending the structure. Thus the vertical through the centre of gravity does not fall within the base. The elastic torque caused because of this bending about the central axis if the tree is given by
$\frac{T\pi {{r}^{4}}}{4R}$ Y is the Young’s modulus, r is the radius of the trunk and R is the radius of curvature of the bent surface along the height of the tress containing the centre of...
An equilateral triangle ABC is formed by two Cu rods AB and BC and one Al rod. It is heated in such a way that the temperature of each rod increases by ∆T. Find the change in the angle ABC.
Answer : The change in angle ABC is calculated using trigonometry. $ \cos \theta =\frac{l_{1}^{2}+l_{3}^{2}-l_{2}^{2}}{2{{l}_{3}}{{l}_{1}}} $ The change in angle ABC is given as when the above...
A steel rod of length 2l, cross-sectional area A and mass M is set rotating in a horizontal plane about an axis passing through the centre. If Y is the Young’s modulus for steel, find the extension in the length of the rod.
Answer : The tensions T(r) and T(r+dr) acting as an external force on the rod at positions A and B are T(r) and T(r+dr). The centrifugal force on the element owing to tension difference is...
a) A steel wire of mass μ per unit length with a circular cross-section has a radius of 0.1 cm. The wire is of length 10 m when measured lying horizontal, and hangs from a hook on the wall. A mass of 25 kg is hung from the free end of the wire. Assuming the wire to be uniform and lateral strains << longitudinal strains, find the extension in the length of the wire. The density of steel is 7860 kg/m3. b) If the yield strength of steel is 2.5 × 108 N/m2, what is the maximum weight that can be hung at the lower end of the wire?
Answer: Consider that dx represents the small element and dm represents the mass. Let L be the length of the wire and x denote the distance from the end where the wire is hung. Let μ be the mass per...
Consider a long steel bar under a tensile stress due to forces F acting at the edges along the length of the bar. Consider a plane making an angle θ with the length. What are the tensile and shearing stresses on this plane?
a) for what angle is the tensile stress a maximum? b) for what angle is the shearing stress a maximum? Answer: According to the question, the force F is applied along the horizontal. Therefore, when...
Two identical solid balls, one of ivory and the other of wet-clay, are dropped from the same height on the floor. Which one will rise to a greater height after striking the flood and why?
Answer : Because the ivory balls are more elastic than the wet clay balls, and they are both dropped from the same height, their velocities shortly before hitting the floor will be the same. The...
A truck is pulling a car out of a ditch by means of a steel cable that is 9.1 m long and has a radius of 5 mm. When the car just begins to move, the tension in the cable is 800 N. How much has the cable stretched?
Answer: According to the question, the length of the steel cable is l = 9.1 m and the radius, r = 5 mm Also, the Tension on the cable = 800 N It is also given that the Young’s modulus is Y = 2 ×...
To what depth must a rubber ball be taken in deep sea so that its volume is decreased by 0.1%.
Answer: According to the question, the bulk modulus of rubber is B = 9.8 × 108 N/m2 The density of seawater is given = 103 kg/m3 0.1% is the percentage decrease in volume We know that the...
A steel rod of length 1 m and area of cross-section 1 cm2 is heated from 0 degrees C to 200 degrees C without being allowed to extend or bend. What is the tension produced in the rod?
Answer: According to the question, the Young’s modulus of steel is Y = 2.0 × 1011 N/m2 The coefficient of thermal expansion is α = 10-5 oC-1 And the length is => L = 1 m Therefore, the area of...
A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by l. Another wire of the same material of length 2L and radius 2r is pulled by a force 2f. Find the increase in length of this wire.
Answer : According to the given figure, the young's modulus is given by the expression : Y = (f/A)(L/l) First case: Let the length of the wire be L and the radius of wire be r. Force applied = f and...
In an experiment to estimate the size of a molecule of oleic acid, 1mL of oleic acid is dissolved in 19mL of alcohol. Then 1mL of this solution is diluted to 20mL by adding alcohol. Now, 1 drop of this diluted solution is placed on water in a shallow trough. The solution spreads over the surface of water forming one molecule thick layer. Now, lycopodium powder is sprinkled evenly over the film we can calculate the thickness of the film which will give us the size of oleic acid molecule.
Read the passage carefully and answer the following questions:
What will be the volume of oleic acid in one drop of this solution?
The volume of oleic acid in one drop is 1/400mL
An artificial satellite is revolving around a planet of mass M and radius R, in a circular orbit of radius r. From Kepler’s third law about the period of a satellite around a common central body, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show using dimensional analysis, that T = k/R √r3/g where k is a dimensionless constant and g is acceleration due to gravity.
Kepler's third law states that, $T^{2} \propto a^{3}$ i.e., square of time period $\left(T^{2}\right)$ of a satellite revolving around a planet, is proportional to the cube of the radius of the...
A physical quantity X is related to four measurable quantities a, b, c and d as follows: 
. The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4%, respectively. What is the percentage error in quantity X? If the value of X calculated on the basis of the above relation is 2.763, to what value should you round off the result.
The given physical quantity is $X=a^{2}b^{3}c^{5/2}d^{-2}$ Percentage error in X is given as (∆x/x)(100) Percentage error in a is given as (∆a/a)(100) = 1% Percentage error in b is given as...
A new system of units is proposed in which unit of mass is α kg, unit of length β m and unit of time γ s. How much will 5 J measure in this new system?
Let Q be the physical quantity as $n_{1}u_{1}=n_{2}u_{2}$ Let $M_{1}$, $L_{1}$, $T_{1}$ be the units of mass, length, and time for the first system. and $M_{2}$,$L_{2}$,$T_{2}$ be the units of mass,...
If the unit of force is 100 N, unit of length is 10 m and unit of time is 100 s, what is the unit of mass in this system of units?
Force [F] is given as 100 N Length [L] is given as 10 m Time [t] is given as 100 s $[F]=[MLT^{2}]$ Substituting the values, we get M = 105 kg
From parallax measurement, the sun is found to be at a distance of about 400 times the earth-moon distance. Estimate the ratio of sun-earth diameters.
The ratio of sun-earth diameter is $D_{sun}/D_{earth}=100$
The radius of an atom is of the order of 1 Å and radius of nucleus is of the order of fermi. How many magnitudes higher is the volume of the atom as compared to the volume of the nucleus?
Radius of atom is given as $1 Å = 10^{-10} m$ Radius of nucleus is known as $1 fermi = 10^{-15} m$ Volume of atom will be $4/3\pi Ra^{3}$ Volume of nucleus will be $4/3\pi Rn^{3}$...
Which of the following are not a unit of time?
a) second
b) parsec
c) year
d) light year
Correct answers are b) parsec and d) light year
If momentum (P), area (A), and time (T) are taken to be fundamental quantities, then energy has the dimensional formula
a) 
b) 
c) 
d) 
Correct answer is d) $P^{1}A^{1/2}T^{-1}$
The mean length of an object is 5 cm. Which of the following measurements is most accurate?
a) 4.9 cm
b) 4.805 cm
c) 5.25 cm
d) 5.4 cm
Correct answer is a) 4.9 cm
You measure two quantities as A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 m. We should report the correct value for √AB as:
a) 1.4 m ± 0.4 m
b) 1.41 m ± 0.15 m
c) 1.4 m ± 0.3 m
d) 1.4 m ± 0.2 m
Correct answer is d) 1.4 m ± 0.2 m
The mass and volume of a body are 4.237 g and 
respectively. The density of the material of the body in correct significant figures is:
a) 
b) 
c) 
d) 
Correct answer is c) $1.7g/cm^{3}$
You are riding in an automobile of mass 
. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags 
when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by 
during one complete oscillation. Estimate the values of (a) the spring constant 
and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports 
.
(a) Mass of the automobile is given as $=3000 \mathrm{~kg}$ The suspension sags by a length of $15 \mathrm{~cm}$ Decrease in amplitude $=50 \%$ during one complete oscillation If each spring's...
An air chamber of volume V has a neck area of cross-section into which a ball of mass 
just fits and can move up and down without any friction. Show that when the ball is pressed down a little and released, it executes SHM. Obtain an expression for the time period of oscillations assuming pressure-volume variations of air to be isothermal [see Figure]
Solution: Volume of the air chamber is given as $\mathrm{V}$ Cross-sectional area of the neck is given as $\mathrm{A}$ Mass of the ball be $m$ The ball is fitted in the neck at position given as...
A cylindrical piece of cork of density of base area A and height h floats in a liquid of density 
. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period 
where 
is the density of cork. (Ignore damping due to viscosity of the liquid)
Base area of the cork is given as $=\mathrm{A}$ Height of the cork is given as $h$ Density of the liquid is given as $\rho_{1}$ Density of the cork is given as $\rho$ In equilibrium: Weight of the...
Answer the following questions:
(a) A man with a wristwatch on his hand falls from the top of a tower. Does the watch give the correct time during the free fall?
(b) What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity?
(a) Wristwatches work on the principle of spring action and are not affected by gravity's acceleration. As a result, the time on the watch will be accurate. (b) The cabin's acceleration owing to...
Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial 
position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: ( 
is in cm and 
is in 
.
(a) 
(b) 
(a) $x=-2 \sin (3 t+\pi / 3)$ $=2 \cos (3 t+\pi / 3+\pi / 2)$ $=2 \cos (3 t+5 \pi / 6)$ On comparing the above equation with the standard equation, $x=A \cos (\omega t+\Phi)$, Amplitude will be $A=2...
In the given figure, let us take the position of mass when the spring is unstreched as 
, and the direction from left to right as the positive direction of -axis. Give as a function of time 
for the oscillating mass if at the moment we start the stopwatch (t 
, the mass is at the maximum compressed position. In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?
Solution: The body is in the left position at maximal compression, with an initial phase of $3 \pi / 2$ rad. Then, $x=a \sin (\omega t+3 \pi / 2)$ $=-a \cos \omega t$ $=-2 \cos 20 t$ As a result,...
A spring having with a spring constant 
is mounted on a horizontal table as shown in Fig. 14.24. A mass of 
is attached to the free end of the spring. The mass is then pulled sideways to a distance of 
and released.
Determine the maximum speed of the mass. Solution: Spring constant is given as $\mathrm{k}=1200 \mathrm{~N} \mathrm{~m}^{-1}$ Mass is given as $\mathrm{m}=3 \mathrm{~kg}$ Displacement is given as...
A spring balance has a scale that reads from 0 to 
. The length of the scale is 
A body suspended from this balance, when displaced and released, oscillates with a period of 
S. What is the weight of the body?
Maximum mass that the scale can rea is given as $M=50 \mathrm{~kg}$ Maximum displacement of the spring = Length of the scale, $I=20 \mathrm{~cm}$ $=0.2 \mathrm{~m}$ Time period is given as $T=0.6...
Which of the following relationships between the acceleration a and the displacement of a particle involve simple harmonic motion?
(a) 
(b) 
The condition of SHM is stated below, Acceleration is directly proportional to negative of displacement of particle. If ' $\mathrm{a}$ ' is the acceleration, $\mathrm{x}$ is the displacement Then,...
Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion (w is any positive constant):
(a) 
(b) 
(a) $\exp \left(-\omega^{2} \mathrm{t}^{2}\right)$ It's a one-time exponential function that doesn't repeat. As a result, the motion is non-periodic. (b) The given function $1+\omega t+\omega^{2}...
Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
(a) the rotation of earth about its axis.
(b) motion of an oscillating mercury column in a U-tube.
(a) The earth's rotation is not a to-and-fro motion around a fixed point. As a result, it is regular but not S.H.M. (b) Simple harmonic motion
Which of the following examples represents periodic motion?
(a) A swimmer completing one (return) trip from one bank of a river to the other and back.
(b) A freely suspended bar magnet displaced from its N-S direction and released.
(a) The motion of the swimmer is not regular. A swimmer's move between the sides of a river is to and fro. It does not, however, have a set duration. This is because the swimmer's back and forth...
What is the Bulk modulus for a perfect rigid body?
Answer: We know that the expression for bulk modulus is given as: Bulk modulus = Stress / Volume strain Bulk Modulus = pV/∆V For a perfectly rigid body, bulk modulus is B = pV/0 B =...
What is the Young’s modulus for a perfect rigid body?
Answer: According to Hooke’s law, we know that the young's modulus is given as : Young’s modulus = Stress/ Longitudinal strain The Young's modulus is calculated as follows when the provided body is...
Identical springs of steel and copper are equally stretched. On which, more work will have to be to done?
Answer: When identical steel and copper springs are stretched equally, force is given as: $ W\alpha \Delta l $ Because the springs are the same, their length and area will likewise be equivalent. $...
Is stress a vector quantity?
Answer : The quantity of stress is neither a scalar nor a vector quantity. It's a tensor quantity, so it's a tensor quantity. This is due to the fact that stress equals the magnitude of the internal...
The Young’s modulus for steel is more than that for rubber. For the same longitudinal strain, which one will have greater tensile stress?
Answer: We know that the expression for Young’s modulus is given as: $ \frac{{{Y}_{steel}}}{{{Y}_{rubber}}}=\frac{Stres{{s}_{steel}}}{Stres{{s}_{rubber}}} $ Steel has a higher tensile stress when...
A copper and a steel wire of the same diameter are connected end to end. A deforming force F is applied to this composite wire which causes a total elongation of 1 cm. The two wires will have
a) the same stress b) different stress c) the same strain d) different strain Answer: The correct answers are a) the same stress d) different strain EXPLANATION - Expression for the internal force...
For an ideal liquid
a) the bulk modulus is infinite b) the bulk modulus is zero c) the shear modulus is infinite d) the shear modulus is zero Answer: The correct answers are a) the bulk modulus is infinite d) the shear...
A rod of length l and negligible mass is suspended at its two ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths. The cross-sectional areas of wires A and B are 1.0 mm2 and 2.0 mm2 respectively.
a) mass m should be suspended close to wire A to have equal stresses in both the wires b) mass m should be suspended close to B to have equal stresses in both the wires c) mass m should be suspended...
A wire is suspended from the ceiling and stretched under the action of a weight F suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight.
a) tensile stress at any cross-section A of the wire is F/A b) tensile stress at any cross-section is zero c) tensile stress at any cross-section A of the wire is 2F/A d) tension at any...
The stress-strain graphs for the two materials are shown in the figure.
a) material (ii) is more elastic than material (i) and hence material (ii) is more brittle b) material (i) and (ii) have the same elasticity and the same brittleness c) material (ii) is elastic over...
A rectangular frame is to be suspended symmetrically by two strings of equal length on two supports. It can be done in one of the following three ways:
The tension in the strings will be a) the same in all cases b) least in a) c) least in b) d) least in c) Answer: The correct answer is c) least in b)
Consider two cylindrical rods of identical dimensions, one of rubber and the other of steel. Both the rods are fixed rigidly at one end to the roof. A mass M is attached to each of the free ends at the centre of the rods.
a) both the rods will elongate but there shall be no perceptible change in shape b) the steel rod will elongate and change shape but the rubber rod will only elongate c) the steel rod will elongate...
A mild steel wire of length 2L and cross-sectional area A is stretched, well within elastic limit, horizontally between two pillars. A mass m is suspended from the mid-point of the wire. Strain in the wire is
Answer : The correct option is (a).
A rigid bar of mass M is supported symmetrically by three wires each of length l. Those at each end are of copper and the middle one is of iron. The ratio of their diameter, if each is to have the same tension, is equal to
Answer : The correct answer is b) Let T be tension in each wire.AS the bar is supported symmetrically by the three wires, therefore extension in each wire is same as Y = FL / AΔL If D is the...
A spring is stretched by applying a load to its free end. The strain produced in the spring is a) volumetric b) shear c) longitudinal and shear d) longitudinal
Answer: The correct answer is c) longitudinal and shear The shape (shear) and length of a spring vary when it is stretched by a load. Shearing and longitudinal strain are therefore produced.
The temperature of a wire is doubled. The Young’s modulus of elasticity a) will also double b) will become four times c) will remain same d) will decrease
Answer : The correct answer is d) will decrease As Y= FL / AΔL when temperature is doubled, ΔL increases and accordingly Y decreases.
The maximum load a wire can withstand without breaking when its length is reduced to half of its original length, will a) be doubled b) be half c) be four times d) remain same
Answer : The correct answer is d) remains same Breaking force = Breaking stress ×Area of the cross-section. The area of cross-section of the wire does not change when the wire is sliced in half. As...
Modulus of rigidity of ideal liquid is a) infinity b) zero c) unity d) some finite small non-zero constant value
Answer : The correct answer is b) zero As we know that η = shearing strain / shearing stress and since liquids cannot sustain shearing stress Therefore, η = 0 in their case.
In deriving Bernoulli’s equation, we equated the work done on the fluid in the tube to its change in the potential and kinetic energy. (a) What is the largest average velocity of blood flow in an artery of diameter 2 × 10–3 m if the flow must remain laminar? (b) Do the dissipative forces become more important as the fluid velocity increases? Discuss qualitatively.
Answer : Answer : (a) If dissipative forces exist, some forces in the liquid flow due to pressure difference are expended against dissipative forces, resulting in a high-pressure drop. (b) Due to...
A truck parked outside a petrol pump blows a horn of frequency 
in still air. The Wind then starts blowing towards the petrol pump at 
Calculate the wavelength, speed, and frequency of the horn’s sound for a man standing at the petrol pump. Is this situation completely identical to a situation when the observer moves towards the truck at 
sand the air is still?
For the standing observer: Frequency is given as $\mathrm{v}_{\mathrm{H}}=200 \mathrm{~Hz}$ Velocity of sound is given as $v=340 \mathrm{~m} / \mathrm{s}$ Speed of the wind is given as $v_{w}=20...
A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 
. During one fast swoop directly toward a flat wall surface, the bat is moving at 
times the speed of sound in the air. What frequency does the bat hear reflected off the wall?
The sound emission frequency of the bat is given as $=40 \mathrm{kHz}$ The velocity of the bat is given as $v_{b}=0.03 \mathrm{v}$ Here, the velocity of the sound in air is $v$ The apparent...
A narrow sound pulse (for example, a short pip by a whistle) is sent across a medium. (a) Does the pulse have a definite (i) frequency, (ii) wavelength, (iii) speed of propagation? (b) If the pulse rate is 1 after every 
, (that is the whistle is blown for a split of second after every ), is the frequency of the note produced by the whistle equal to 
or 
?
(a) The speed of propagation is known, and it is the same as the speed of sound in air. The wavelength and frequency of the signal will be uncertain. (b) The note emitted by a whistle does not have...
A train, standing in a station-yard, blows a whistle of frequency 
in still air. The wind starts blowing in the direction from the yard to the station with a speed of 
. What are the frequency, wavelength, and speed of sound for an observer standing on the station’s platform? Is the situation exactly identical to the case when the air is still and the observer runs towards the yard at a speed of ? The speed of sound in still air can be taken as 
Frequency of the whistle is given as $400 \mathrm{~Hz}$ Speed of wind is given as $\mathrm{v}_{\mathrm{w}}=10 \mathrm{~m} / \mathrm{s}$ Speed of sound in still air is given as $v= 340 \mathrm{~m} /...
Explain how:
In a dispersive medium, the shape of a pulse propagating through it gets distorted.
A pulse is made up of electromagnetic waves with different wavelengths. In a dispersive medium, these waves flow at various speeds. Its shape is distorted as a result of this.
Guitar strings 
and 
striking the note ‘Ga’ are a little out of tune and give beats at 
. When the string 
is slightly loosened and the beat frequency becomes 
. Given that the original frequency of is 
, find the frequency of .
Frequency of $\mathrm{X}$ is given as $\mathrm{f}_{\mathrm{x}}=324 \mathrm{~Hz}$ Frequency of $Y$ is given as $f_{Y}$ Frequency of the beat is given as $\mathrm{n}=6 \mathrm{~Hz}$ Also,...
A steel bar of length 
is nailed at its midpoint. The fundamental frequency of the longitudinal vibrations of the rod is 
. At what speed will the sound be able to travel through steel?
Length is given as $I=200 \mathrm{~cm}=2 \mathrm{~m}$ Fundamental frequency of vibration is given as, $\mathrm{v}_{\mathrm{F}}=2.53 \mathrm{kHz}=2.53 \times 10^{3} \mathrm{~Hz}$ The bar is then...
A string clamped at both its ends is stretched out, it is then made to vibrate in its fundamental mode at a frequency of 
. The linear mass density of the string is 
m and its mass is 
kg. Calculate:
(i) the velocity of a transverse wave on the string,
(ii) the tension in the string.
Mass of the string is given as $m=2 \times 10^{-2} \mathrm{~kg}$ Linear density of the string is given s $=4 \times 10^{-2} \mathrm{~kg}$ Frequency is given as $\mathrm{v}_{\mathrm{F}}=45...
Present below are functions of 
and 
to describe the displacement (longitudinal or transverse) of an elastic wave. Identify the ones describing ( a ) a stationary wave, ( b ) a travelling wave and ( c) neither of the two:
(ii) 
(i) The harmonic terms $\omega t$ and $kx$ in the combination of $k x-w t$ explain a traveling wave in this equation. (ii) The harmonic terms $\omega t$ and $kx$ exist individually in the equation....
For the wave, 
plot the displacement ( 
) versus (t) graphs for 
0,2 and 
.
(i) Give the shapes of these plots.
(ii) With respect to which aspects (amplitude, frequency or phase) does the oscillatory motion in a travelling wave differ from one point to another?
Given wave is, $y(x, t)=3 \sin (36 t+0.018 x+\pi / 4)$.....(1) Putting $x=0$, the equation becomes: $y(0, t)=3 \sin (36 t+0+\pi / 4)$.....(2) Also, $\omega=2 \pi / \mathrm{t}=36 \mathrm{rad} /...
A transverse harmonic wave on a wire is expressed as:
(i) Is it a stationary wave or a travelling one?
ii) If it is a travelling wave, give the speed and direction of its propagation.
[ and 
are in 
and in seconds. Assume the left to right direction as the positive direction of ![\mathrm{x}]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7eec0f19e3a8a19059d43c95ee5abebd_l3.png "Rendered by QuickLaTeX.com")
Given function is, $(x, t)=3 \sin (36 t+0.018 x+\pi / 4)$ i) The equation of a progressive wave travelling from right to left is known as, $y(x, t)=a \sin (\omega t+k x+\Phi)$ On comparing equation...
A bat emits ultrasonic sound of frequency 
in air. If the sound meets a water surface, what is the wavelength of (a) the reflected sound, (b) the transmitted sound? Speed of sound in air is and in water 
Frequency of the ultrasonic sound is given as $\mathrm{v}=1000 \mathrm{kHz}=10^{6} \mathrm{~Hz}$ Speed of sound in air is given as $v_{A}=340 \mathrm{~m} / \mathrm{s}$ As we know, (a) The wavelength...
Steel wire has a length of 
and a mass of 
What should be the tension in the wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air at 
Length of the steel wire is given as $I=12 \mathrm{~m}$ Mass of the steel wire is given as $\mathrm{m}=2.0 \mathrm{~kg}$ Velocity of the transverse wave is given as $\mathrm{v}=343 \mathrm{~m} /...
A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg. The area of cross-section of the piston carrying the load is 425 cm2. What maximum pressure would the smaller piston have to bear ?
Answer : Given: according to the question, the maximum mass that can be lifted is given as m = 3000 kg and the area of a cross-section of the load-carrying piston is A = 425 cm2 = 425 × 10-4 m2...
The triple points of neon and carbon dioxide are 24.57 K and 216.55 K, respectively. Express these temperatures on the Celsius and Fahrenheit scales.
Solution: Given: Kelvin and Celsius scales are related as: $\mathrm{T}_{\mathrm{C}}=\mathrm{T}_{\mathrm{K}}-273.15 \ldots . \ldots . \ldots . \ldots(1)$ We know that,...
The Marina trench is located in the Pacific Ocean, and at one place it is nearly eleven km beneath the surface of the water. The water pressure at the bottom of the trench is about 
Pa. A steel ball of initial volume 
is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches the bottom?
Water pressure at the bottom of the trench is given as $\mathrm{p}=1.1 \times 10^{8} \mathrm{~Pa}$ Initial volume of the steel ball is given as $V=0.32 \mathrm{~m}^{3}$ Bulk modulus of steel is...
Determine the volume contraction of a solid copper cube, 
on an edge, when subjected to a hydraulic pressure of 
.
Side of the copper cube is given as $a=10 \mathrm{~cm}$ Therefore, Volume of the copper cube will be, $\mathrm{V}=\mathrm{a}^{3}=10^{-3} \mathrm{~m}^{3}$ Hydraulic pressure is given as...
Compute the bulk modulus of water from the following data: Initial volume = 
litre, Pressure increase 
, Final volume 
litre. Compare the bulk modulus of water with that of air (at constant temperature). Explain in simple terms why the ratio is so large.
Initial volume is given as $V_{1}=100.0$ litre $=100.0 \times 10^{-3} \mathrm{~m}^{3}$ Final volume is given as $V_{2}=100.5$ litre $=100.5 \times 10^{-3} \mathrm{~m}^{3}$ $=101.3 \times 10^{5}...
Area of the copper piece is given as $A=19.1 \times 10^{-3} \times 15.2 \times 10^{-3}=2.9 \times 10^{-4} \mathrm{~m}^{2}$ Tension force applied on the piece of copper is given as $\mathrm{F}=44,500...
Read the following two statements below carefully and state, with reasons, if it is true or false.(a) The Young’s modulus of rubber is greater than that of steel;(b) The stretching of a coil is determined by its shear modulus.
(a) True. Stretching a coil does not affect its length; instead, it changes its shape, which requires shear modulus. (b) False. This is because rubber has more strain than steel for the same amount...
Figure below shows the strain-stress curve for a given material. What are (a) Young’s modulus and (b) approximate yield strength for this material?
Solution: (a) Young's modulus, $Y=\frac{Stress}{Strain}$ $=150 \times 10^{6} / 0.002$ $=150 \times 10^{6} / 2 \times 10^{-3}$ $=75 \times 10^{9} \mathrm{Nm}^{-2}$ $=75 \times 10^{10}...
A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Give the magnitude and direction of the acceleration of the body.
Given, m = 5 kg (mass) F1 = 8N and F2 = 6N are two different forces. The force exerted by the body as a result of this.
One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is : (i) T (ii) T – mv2/l (iii) T + mv2/l (iv) 0 T is the tension in the string. [Choose the correct alternative].
T is the particle's net force, and it is directed towards the centre. It gives the particle the centrifugal force it needs to travel in a circle.
A thin circular loop of radius R rotates about its vertical diameter with an angular frequency ω. Show that a small bead on the wire loop remains at its lowermost point for ω ≤ √g / R . What is the angle made by the radius vector joining the centre to the bead with the vertically downward direction for ω = √2g/ R ? Neglect friction.
Let θ be the angle made by the radius vector joining the bead and the centre of the wire with the downward direction. Let, N be the normal reaction mg = N cosθ —–(1) mrω2 = Nsinθ —– (2) (or) m...
A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min. The coefficient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?
m = 70 kg m The drum's radius is 3 metres. = 0.15 is the coefficient of friction between the wall and his clothes. The number of revolutions per minute of a hollow cylindrical drum is 200/60 = 10/3...
You may have seen in a circus a motorcyclist driving in vertical loops inside a ‘death well’ (a hollow spherical chamber with holes, so the spectators can watch from outside). Explain clearly why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m?
When the biker reaches the top of the death-well, the usual response R acted on him by the chamber's roof acts downwards. His weight mg also has a negative effect. These two forces balance the...
A disc revolves with a speed of 33⅓ rpm and has a radius of 15 cm. Two coins are placed at 4 cm and 14 cm away from the centre of the record. If the coefficient of friction between the coins and record is 0.15, which of the coins will revolve with the record?
The disc's revolution speed is 33. 13 rpm = 100/3 rpm = 100/3 rpm = 100/ (3 x 60) rps = 5/9 rps 220/63 rad/s = 2v = 2 x (22/7)x (5/9) The centripetal force is produced by the frictional force mv2/r...
The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in Fig. The coefficient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with 2 ms-2. At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).
F = ma = 40 x 2 = 80 N is the force experienced by the box. Ff = mg = 0.15 x 40 x 10 = 60 N Frictional force F – Ff = 80 – 60 = 20 N Net force = F – Ff = 80 – 60 = 20 N In the box, a =20/40(Net...
A block of mass 15 kg is placed on a long trolley. The coefficient of static friction between the block and the trolley is 0.18. The trolley accelerates from rest with 0.5 ms-2 for 20 s and then moves with uniform velocity. Discuss the motion of the block as viewed by (a) a stationary observer on the ground, (b) an observer moving with the trolley.
The block's mass is 15 kg. Static friction coefficient between the block and the trolley, p= 0.18 The trolley accelerates at a rate of 0.5 m/s2. (a) The force experienced by the block, F = ma = 15 x...
Two bodies A and B of masses 5 kg and 10 kg in contact with each other rest on a table against a rigid wall (Fig.). The coefficient of friction between the bodies and the table is 0.15. A force of 200 N is applied horizontally to A. What are (a) the reaction of the partition (b) the action-reaction forces between A and B? What happens when the wall is removed? Does the Solution to (b) change, when the bodies are in motion? Ignore the difference between μs and μk.
mA = 5 kg is the mass of the body. mB = ten kilogrammes of body mass 200 N Applied Force s = 0.15 is the coefficient of friction between the bodies and the table. (a) The...
A monkey of mass 40 kg climbs on a rope (Fig.) which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey (a) climbs up with an acceleration of 6 ms-2 (b) climbs down with an acceleration of 4 ms-2 (c) climbs up with a uniform speed of 5 ms-1 (d) falls down the rope nearly freely under gravity? (Ignore the mass of the rope).
The monkey weighs 40 kg. Tmax=600 N is the maximum tension the rope can sustain. (a) When the monkey climbs at a speed of 6 metres per second, T – mg = ma Tension T – mg = ma T...
A block of mass 25 kg is raised by a 50 kg man in two different ways as shown in Fig. What is the action on the floor by the man in the two cases? If the floor yields to a normal force of 700 N, which mode should the man adopt to lift the block without the floor yielding?
The block's mass is 25 kg. The man's weight is 50 kg. Gravitational acceleration = 10 m/s2 F = 25 x 10 = 250 N is the block's weight. W = 50 x 10 = 500 N is the man's weight. In the first example,...
An aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at 15°. What is the radius of the loop?
720 km/h = 720 x (5/18) = 200 m/s is the speed of the aeroplane doing the horizontal loop. The banking angle is 15 degrees. We have tan= v2/rg. (200 x 200)/(10 x tan 150) = (200 x 200)/ (10 x...
Ten one rupee coins are put on top of one another on a table. Ten one rupee coins are put on top of one Each coin has a mass of m kg. Give the magnitude and direction of the reaction of the sixth coin on the seventh coin.
(c) The sixth coin is pressed against the four coins above it, which are pulling it downward. The 6th coin has a total downward force of 4mg. The 6th coin will exert a reaction force upwards,...
Ten one rupee coins are put on top of one another on a table. Each coin has a mass of m kg. Give the magnitude and direction of the force on the 7th coin by the eighth coin
The eighth coin is already weighed down by the weight of two coins above it, as well as its own. As a result, the force exerted on the seventh coin by the eighth coin will be equal to the force...
Ten one rupee coins are put on top of one another on a table. Each coin has a mass of m kg. Give the magnitude and direction of the force on the 7th coin (counted from the bottom) due to all coins above it.
The weight of the three coins above it exerts a force on the seventh coin. One coin has a mass of milligrammes. As a result, three coins weigh 3mg. The force applied to the seventh coin is (3mg)N,...
A stream of water flowing horizontally with a speed of 15 m/s pushes out of a tube of cross-sectional area 10-2 m2 and hits at a vertical wall nearby. What is the force exerted on the wall by the impact of water, assuming that it does not rebound?
Flowing water speed, v=15 m/s A= 10-2 m2 is the cross-sectional area of the tube. The distance travelled in one second is equal to the velocity v. 1000 kgm-3 is the density of water. ρ...
A helicopter of mass 1000 kg rises with a vertical acceleration of 15 ms-2. The crew and the passengers weigh 300 kg. Give the magnitude and direction of (a) force on the floor by the crew and passengers, (b) the action of the rotor of the helicopter on surrounding air (c) force on the helicopter due to the surrounding air
Helicopter mass is 1000 kg. The combined weight of the crew and passengers is 300 kg. a = 15 ms-2 and g = 10 ms-2 are the vertical accelerations. The system's total mass, mi = 1000 + 300 = 1300 Kg...
. A stone of mass m tied to the end of a string is revolving in a vertical circle of radius R. The net force at the lowest and highest points of the circle directed vertically downwards are: (choose the correct alternative).
T1 and v1 denote the tension and speed at the lowest point. T2 and v2 denote corresponding values at the highest point. (mg – T1) is the net force at the lowest position, and (mg + T2) is the net...
Explain why it is easier to pull a lawnmower than to push it.
The vertical component of the applied force acts upwards when the lawnmower is pushed. The lawnmower's effective weight is reduced as a result. When pushing the lawn mower, the vertical component...
If in problem 21, the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks: (a) the stone moves radially outwards, (b) the stone flies off tangentially from the instant the string breaks, (c) the stoneflies off at an angle with the tangent whose magnitude depends on the speed of the particle?
(b) The velocity of the circular motion will be tangential at each location. According to Newton's first rule of motion, if the rope snaps suddenly, the stone will move in a tangential path.
A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 ms-1.What is the recoil speed of the gun?
m = 0.020 kg is the mass of the shell. M is the gun's mass, which is 100 kilogrames. The shell's speed is 80 m/s. The shell's and gun's initial velocity is both zero. As a result, the system's...
Two billiard balls, each of mass 0.05 kg, moving in opposite directions with speed 6 ms-1 collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?
Each ball has a mass of 0.05 kg. Each ball's initial velocity is 6 m/s. Before the impact, each ball's initial momentum 0.3 kg m/s = 0.05 x 6 The direction of motion of the balls changes after the...
A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei, the products must move in opposite directions.
Let m1, m2 be the masses of the two daughter nuclei, and v1, v2 be the daughter nuclei's respective velocities. Let m be the parent nucleus's mass. After disintegration, total linear momentum = m1v1...
Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses and the tension in the string when the masses are released.
According to the question, m1 = 8 kg m2 = 12 kg Tension = T The heavier mass m2 will move downwards and the smaller mass m1 will move upwards. On Applying Newton’s second law, For mass m1: T – m1g =...
A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 ms-1. What is the trajectory of the bob if the string is cut when the bob isat its mean position?
The bob has a horizontal velocity in its mean position. The bob will act like a projectile if the string is severed, and it will fall to the earth after travelling a parabolic route.
A rocket with a lift-off mass of 20,000 kg is blasted upwards with an initial acceleration of 5.0 ms-2. Calculate the initial thrust (force) of the blast.
Given, m = 20000 kg = 2 x 104 kg Initial acceleration = 5 ms-2 g = 9.8 m/s2 The initial thrust (force) should provide a 5 ms-2 upward acceleration and should overcome gravity. As a result of the...
A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Give the magnitude and direction of the acceleration of the body.
According to the question, m = 5 kg F1 = 8N ,F2 = 6N Resultant force of the body F = \sqrt{F_{1}^{2}+F_{2}^{2}}=\sqrt{8^{2}+6^{2}}= \sqrt{64+36}=10NF=F12+F22=82+62=64+36=10N , a = F/m a = 10/ 5...
One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is : (i) T (ii) T – mv2/l (iii) T + mv2/l (iv) 0 T is the tension in the string. [Choose the correct alternative].
T is the particle's net force, and it is directed towards the centre. It gives the particle the centrifugal force it needs to travel in a circle.