Obtain the corresponding simple harmonic motions of the $x$-projection of the radius vector of the revolving particle $P$, in each case. Solution: (a) Time period is given as $t=2 \mathrm{~s}$...
, 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 isSolution: Distance travelled by the mass sideways is given as $a=2.0 \mathrm{~cm}$ Angular frequency of oscillation can be calculated as, $\omega=\sqrt{k} / \mathrm{m}$ $=\sqrt{1200 / 3}$...
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<br>(i) the frequency of oscillations, (ii) maximum acceleration of the mass Solution: Spring constant is given as $\mathrm{k}=1200 \mathrm{~N} \mathrm{~m}^{-1}$ Mass is given as...
If the initial (t 
) position of the particle is 
and its initial velocity is 
, what are its amplitude and initial phase angle? The angular frequency of the particle is 
. If instead of the cosine function, we choose the sine function to describe the SHM: 
, what are the amplitude and initial phase of the particle with the above initial conditions. Solution:At positlon, t = 0, The given function is $x(t)=A \cos (\omega t+\phi).....(1)$ $\begin{array}{l} 1=A \cos (\omega \times 0+\phi)=A \cos \phi \\ A \cos \phi=1 \end{array}$ Differentiating equation...
of a particle involve simple harmonic motion?
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, for...
apart. Take the direction from 
to 
as the positive direction and give the signs of velocity, acceleration and force on the particle when it is
away from B going towards (a) Negative, Zero, Zero A basic harmonic motion is being performed by the particle. The particle's mean location is denoted by $O$. Its highest velocity is at the mean position $O$. Because the...
apart. Take the direction from to as the positive direction and give the signs of velocity, acceleration and force on the particle when it is,(a) Zero, Positive, Positive Points A and B are the path's two ends, with A-B=10cm and'O' being the path's halfway. Between the end locations, a particle moves in a linear simple harmonic motion....
(a) $3 \cos [4 \pi-2 \omega t]=3 \cos [2 \omega t-\pi / 4]$ The equation can be written in the form $\cos (\omega t+\phi)$. It is S.H.M with the period $2 \pi / 2 \omega=\pi / \omega$ (b) $\cos...
(a) $\sin \omega t-\cos \omega t$ =2[(1/2)sinωt-(1/2)cosωt] =\sqrt{2}[(1 / \sqrt{2}) \sin \omega t-(1 / \sqrt{2}) \cos \omega t] $=\sqrt{2}[\sin \omega t \times \cos (\pi / 4)-\cos...
plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?(a) Because the motion is repeated in only one position, the depicted graph does not illustrate periodic motion. The full motion during one period must be repeated successively for a periodic...
plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?(a) Motion is not periodic since it does not repeat itself after a set length of time. (b) The following graph depicts a periodic motion that repeats every 2 seconds.
(a) Simple harmonic motion (b) SHM is not periodic, although general vibrations of a polyatomic molecule about its equilibrium position are. The inherent frequencies of a polyatomic molecule are...
(a) The rotation of a hydrogen molecule around its mass centre is periodic. This is due to the fact that when a hydrogen molecule spins about its centre of mass, it returns to the same location...
for 
of oxygen gas at two different temperatures.(a) What does the dotted plot signify? (b) Which is true: $\mathbf{T}_{1}>\mathbf{T}_{2}$ or $\mathbf{T}_{1}<\mathbf{T}_{2}$ ? Solution: (a) The dotted plot is perpendicular to the x-axis,...
Diameter of an oxygen molecule is given as $d=3 \AA$ Radius will be, $r=d / 2$ $r=3 / 2=1.5 \AA=1.5 \times 10^{-8} \mathrm{~cm}$ Actual volume occupied by 1 mole of oxygen gas at STP is given as...
in still air.
(ii) runs away from him at 
.![\mathbf{3 4 0 \mathrm { m } / \mathrm { s } \text { ] }}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f3e8ca26b9dfd0f318b50c1ded0b4984_l3.png "Rendered by QuickLaTeX.com")
Frequency of the horn is given as $\mathrm{v}_{\mathrm{H}}=200 \mathrm{~Hz}$ Velocity of the man is given as $\mathrm{v}_{\mathrm{T}}=20 \mathrm{~m} / \mathrm{s}$ Velocity of sound is given as...
, and that of the 
wave is 
. A seismograph records and 
waves from an earthquake. The first P wave arrives 4 min before the first 
wave. Assuming the waves travel in a straight line, at what distance does the earthquake occur?Let $S$ and $P$ have speeds of $v_{1}$ and $v_{2}$, respectively. The $S$ and $P$ waves take $t_{1}$ and $t_{2}$ seconds to reach the position of the seismograph, respectively. $I=v_{1} t_{1}=v_{2}...
kHz. An enemy submarine moves towards the SONAR with a speed of 
. What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be 
.Frequency of the SONAR system is given as $\mathrm{f}=40 \mathrm{kHz}=40 \times 10^{3} \mathrm{~Hz}$ Speed of sound in water is given as $v=1450 \mathrm{~m} / \mathrm{s}$ Speed of the enemy...
is connected to an electrically driven tuning fork of frequency 
. The other end passes over a pulley and is tied to a pan containing a mass of 
. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At 
, the left end (fork end) of the string has zero transverse displacement 
and is moving along positive 
-direction. The amplitude of the wave is 
. Write down the transverse displacement y as a function of and that describes the wave on the string.Linear mass density of the string is given as $\mu=8.0 \times 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$ Frequency of the tuning fork is given as $=256 \mathrm{~Hz}$ Mass on the pan is given as $90...
, and 
? Is this velocity equal to the velocity of wave propagation? point at 
and 
(a) The travelling harmonic wave is given by, $y(x, t)=7.5 \sin (0.0050 x+12 t+\pi / 4)$ At $x=1 \mathrm{~cm}$ and $\mathrm{t}=1 \mathrm{~s}$ $y(1,1)=7.5 \sin (0.0050(1)+12(1)+\pi / 4)$ $=7.5 \sin...
in still air. (i) What is the frequency of the whistle for a platform observer when the train (a) approaches the platform with a speed of 
, (b) recedes from the platform with a speed of ? (ii) What is the speed of sound in each case? The speed of sound in still air can be taken as 
.Frequency of the whistle is given as $=400 \mathrm{~Hz}$ Speed of sound in still air is given as $=340 \mathrm{~m} / \mathrm{s}$ (i) (a)Train approaches the platform at a speed given as...
(i) Overtones are produced differently by the guitar and the violin. Even though the notes from a guitar and a violin vibrate at the same frequencies, it is possible to distinguish between them....
(i) An antinode is a place where the pressure is lowest and the vibration amplitude is highest. A node, on the other hand, is a place where pressure is highest and vibration amplitude is lowest....
long tube is closed. Find the harmonic mode of the tube that will be resonantly excited by a source of frequency 
. If both the ends are open, can the same source still produce resonance in the tube? (Sound travels in air at 
).Length of the pipe is given as $I=20 \mathrm{~cm}=0.2 \mathrm{~m}$ Frequency of the source is given as $\mathrm{n}^{\text {th }}$ Normal mode of frequency is given as $\mathrm{v}_{\mathrm{N}}=430...
long pipe with a movable piston at one end and an opening at the other will be in resonance with a tuning fork vibrating at 
, if the length of the pipe is 
or 
. Calculate the speed of sound in air. Neglect the edge effects.Frequency of the turning fork is given as $\mathrm{v}_{\mathrm{F}}=340 \mathrm{~Hz}$ Length of the pipe is given as $l_{1}=0.255 \mathrm{~m}$ Due to the presence of a piston at one end, the supplied...
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:
(i) Because the harmonic terms $\omega t$ and $k x$ exist individually, this equation depicts a stationary wave. (ii) There are no harmonic terms in this equation. As a result, it is neither a...
away from one end?(a) Because both ends of the wire are clamped, the ends act as nodes, and the entire wire vibrates as a single segment. Thus, (i) Except at the wire's ends, where the frequency is 0, all of the...
The mass of the wire is 
and its length is 
. are in meters and in secs]As we know, The standard equation of a stationary wave is known as, $y(x, t)=2 a \sin k x \cos w t$ Given equation is, $y(x, t)=0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$ It is...
The mass of the wire is and its length is . As we know, The standard equation of a stationary wave is known as, $y(x, t)=2 a \sin k x \cos w t$ Given equation is, $y(x, t)=0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$ It is...
. What is the phase difference between the oscillatory motion of two points separated by a distance of:
, 
and are in 
and is in secs ![]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-478d84af1027ee3593251b323a3fb181_l3.png "Rendered by QuickLaTeX.com")
.Equation for a travelling harmonic wave is given as, $\begin{array}{l} y(x, t)=2.0 \cos 2 \pi(10 t-0.0080 x+0.35) \\ =2.0 \cos (20 \pi t-0.016 \pi x+0.70 \pi) \end{array}$ where, Propagation...
. What is the phase difference between the oscillatory motion of two points separated by a distance of:
, and are in and is in secs .Equation for a travelling harmonic wave is given as, $\begin{array}{l} y(x, t)=2.0 \cos 2 \pi(10 t-0.0080 x+0.35) \\ =2.0 \cos (20 \pi t-0.016 \pi x+0.70 \pi) \end{array}$ where, 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, $(x, t)=3 \sin (36 t+0.018 x+\pi / 4)$ The smallest distance between two adjacent crests in the wave can be calculated as, $\lambda=2 \pi / \mathrm{k}=2 \mathrm{~m} / 0.018$ $=349...
and are in and in seconds. Assume the left to right direction as the positive direction of Given function is, $(x, t)=3 \sin (36 t+0.018 x+\pi / 4)$ i) Amplitude of the wave is given as $a=3 \mathrm{~cm}$ Frequency of the wave can be calculated as $v=\omega / 2 \pi$ $36 / 2 \pi=5.7...
is used to locate tumours in tissues. If the speed of sound is 
in a certain tissue, calculate the wavelength of sound in this tissue.Speed of sound in the tissue is given as, $v_{T}=2 \mathrm{~km} / \mathrm{s}=2 \times 10^{3} \mathrm{~m} / \mathrm{s}$ Operating frequency of the scanner is given as $\mathrm{v}=4.2 \mathrm{MHz}=4.2...
represents a wave travelling in one direction, where and must appear in the combination 
or 
or i.e. 
Is the converse true? Can the following functions for y possibly represent a travelling wave: 
![\log \left[(x+v t) / x_{0}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-99d2bcfc07e0da1a668137fffad738d8_l3.png "Rendered by QuickLaTeX.com")
No, the opposite is not true, because a wave function representing a travelling wave must have a finite value for all $x$ and $t$ values. None of the functions above satisfy the criteria, hence none...
explain why the speed of sound in air increases with humidity.Given values are, $v=\sqrt{\frac{\gamma P}{\rho}}$ $\Rightarrow \mathrm{P}=\frac{\rho R T}{M}$ $\Rightarrow \frac{P}{\rho}=\frac{R T}{M}$ The effective density of the air decreases as humidity...
explain why the speed of sound in airGiven values are, $v=\sqrt{\frac{\gamma P}{\rho}}$ $\Rightarrow \mathrm{P}=\frac{\rho R T}{M}$ $\Rightarrow \frac{P}{\rho}=\frac{R T}{M}$ (a) For a gas at a constant temperature, $\frac{P}{\rho}=...
splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is 
? 
Height of the bridge is given as $s=300 \mathrm{~m}$ Initial velocity of the stone is given as $u=0$ Acceleration is known as $a=g=9.8 \mathrm{~m} / \mathrm{s}^{2}$ Speed of sound in air is given as...
is under a tension of 
. The length of the stretched string is 
. If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?Mass of the string is given as $M=2.50 kg$ Tension in the string is given as $T=200 N$ Length of the string is given as $\mid=20.0 m$ Mass per unit length will be, $\mu=\mathrm{M} / \mathrm{I}=5 /...
and length 
is stretched ( not beyond its elastic limit ) horizontally between two columns. If a 
mass is hung at the midpoint of the wire, find the depression at the midpoint.Solution: Let $Y Z$ be a mild steel wire with a cross sectional area of $A=0.60 \times 10^{-2} cm^{2}$ and a length of 2m. As indicated in the image, a mass of $m=100g=0.1kg$ is hanged from the...
What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 
Pa? Assume that each rivet is to carry one-quarter of the load.Diameter of the metal strips is given as $6 \mathrm{~mm}=6 \times 10^{-3} \mathrm{~m}$ Radius will be then, $r=3 \times 10^{-3} \mathrm{~m}$ Shearing stress on the rivet is given as $6.9 \times...
having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown in the figure. The cross-sectional areas of wires and are 
and 
, respectively. At what point along the rod should a mass 
be suspended in order to produce (a) equal stresses and (b) equal strains in both steel and aluminium wires.Solution: Cross-sectional area of wire A is given as $a_{1}=1.0 \mathrm{~mm}^{2}=1.0 \times 10^{-6} \mathrm{~m}^{2}$ Cross-sectional area of wire B is given as $a_{2}=2 m m^{2}=2 \times 10^{-6}...
The diameter of the flat faces at the narrow end of the anvil is given as, $d=0.50mm=0.5\times 10^{-3} m$ Radius will be, $r=d/2=0.25\times 10^{-3} m$ Compressional force is given as $F=50000N$...
?Volume of water is given as $V=1$ litre Water should be compressed by $0.10 \%$ is given The fractional change in volume will be, $\Delta \mathrm{V} N=(0.1 / 100) \times 1=10^{-3}$ Bulk modulus,...
atm, given that its density at the surface is 
?Let the depth be 'd' Pressure at the given depth is given as $p=60\times1.01\times10^{5}Pa$ Density of water at the surface is given as $\rho_{1}=1.03\times10^{3}$ $kg$ $m^{3}$ Let $\rho_{2}$ be the...
is supported symmetrically by three wires each 
long. Those at each end are of copper and the middle one is of iron. Determine the ratios of their diameters if each is to have the same tension.The extension of each wire will be the same because the stress on the wires is the same. Now that the wires are the same length, the tension on them will be the same. Now, we know: $Y=Stress /...
supports a chairlift at a ski area. If the maximum stress is not to exceed 
What is the maximum load the cable can support?Radius of the steel cable is given as $r=1.5 \mathrm{~cm}=0.015 \mathrm{~m}$ Cross-sectional area of the cable will be, $\pi r^{2}=3.14 \times(0.015)^{2}$ $=7.06 \times 10^{-4} \mathrm{~m}$ Maximum...
. The inner and outer radii of each column are 
and 
respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column.Mass of the big structure is given as $M=50,000 \mathrm{~kg}$ Total force exerted on the four columns will be equal to the total weight of the structure, that is, $50000 \times 9.8 \mathrm{~N}$ The...
long. One face of the cube is firmly fixed to a vertical wall. A mass of 
is then attached to the opposite face of the cube. The shear modulus of aluminium is 
. What is the vertical deflection of this face?Edge of the aluminium cube is given as $L=10 \mathrm{~cm}=10 / 100=0.1 \mathrm{~m}$ Area of each face wil be, $A=(0.1)^{2}=0.01 \mathrm{~m}^{2}$ Mass attached to the opposite face of the cube is...
, one made of steel and the other made of brass are loaded as shown in Fig. The unloaded length of steel wire is 
and that of brass wire is 
. Compute the elongations of the steel and the brass wires. [Young’s modulus of steel is 
![\left.10^{11} \mathrm{~Pa} .\left(1 \mathrm{~Pa}=1 \mathrm{~N} \mathrm{~m}^{2}\right)\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-36c8cbb599d2f5fc96ae57f00cbbd2ee_l3.png "Rendered by QuickLaTeX.com")
Diameter of the two wires is given as $d=0.25 \mathrm{~m}$ Radius of the wires is given as $r=d / 2=0.125 \mathrm{~cm}$ Unloaded length of the steel wire is given as $l_{1}=1.5 \mathrm{~m}$ Unloaded...
and are shown in the figure below.(a) Which of the materials has the greater Young's modulus? (b) Which of the two is the stronger material? Solution: (a) We can observe from the graphs that for a given strain, $A$ has a higher...
and cross-sectional area 
stretches by the same amount as a copper wire of length 
and cross-sectional area of 
under a given load. What is the ratio of Young’s modulus of steel to that of copper?Length of the steel wire is given as $l_{1}=4.7 \mathrm{~m}$ Cross-sectional area of the steel wire is given as $a_{1}=3.0 \times 10^{-5} \mathrm{~m}^{2}$ Length of the copper wire is given as...
with a mass of 
. A child whose mass is 20 kg runs on the trolley with a speed of 
from one end to other which is 
. The speed is relative to the trolley in the direction opposite to its motion. Find the final speed of the trolley and the distance the trolley moved from the time the child began to run.Mass is given as $m=200 \mathrm{Kg}$ Speed is given as $v=36 \mathrm{~km} / \mathrm{h}=10 \mathrm{~m} / \mathrm{s}$ Mass of boy is given as $=20 \mathrm{Kg}$ Initial momentum will be, $(M+m) v$...
falls from the ceiling of an elevator moving down with a uniform speed of 
. It hits the floor of the elevator (length of elevator 
) and does not rebound. What is the heat produced by the impact? Would your answer be different if the elevator were stationary?Mass of the bolt is given as $m=0.3 \mathrm{~kg}$ Potential energy of the bolt is given as $m g h=0.3 \times 9.8 \times 3=8.82\rfloor$ The bolt does not return to its original position. As a result,...
block situated on a rough incline is connected to a spring of spring constant 100 
as shown in Fig. The block is released from rest with the spring in the unstretched position. The block moves down the incline before coming to rest. Find the coefficient of friction between the block and the incline. Assume that the spring has a negligible mass and the pulley is frictionless.Solution: Spring constant is given as $\mathrm{k}=100 \mathrm{~N} \mathrm{~m}^{m}$ Displacement in the block is given as $\mathrm{x}=10 \mathrm{~cm}=0.1 \mathrm{~m}$ At equilibrium: Normal reaction...
and horizontal speed 
strikes a block of wood of mass 
and instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. Calculate the height to which the block rises. Also, estimate the amount of heat produced in the block.Mass of the bullet is given as $m_{1}=0.012 \mathrm{~kg}$ Initial speed of the bullet is given as $u_{1}=70 \mathrm{~m} / \mathrm{s}$ Mass of the wooden block is given as $m_{2}=0.4 \mathrm{~kg}$...
each time. Assume that the potential energy lost each time she lowers the mass is dissipated. (a) How much work does she do against the gravitational force? (b) Fat supplies 
of energy per kilogram which is converted to mechanical energy with a 
efficiency rate. How much fat will the dieter use up?Mass is given as $\mathrm{m}=10 \mathrm{~kg}$ Height to which the mass is lifted is given as $h=0.5 \mathrm{~m}$ Number of times is hiven as $n=1000$ (a) Work done against gravitational force can be...
travels in a straight line with velocity 
where 
. What is the work done by the net force during its displacement from to 
m?Let the mass of the body be $m$ $m=0.5 \mathrm{~kg}$ Velocity of the body is represented by $v=a x^{3 / 2}$ where, $a=5 \mathrm{~m}^{-1 / 2} \mathrm{~s}^{-1}$. Initial velocity at $x=0$ will be...
, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 
of its initial energy against air resistance?Length of the pendulum is given as $\mid=1.5 \mathrm{~m}$ Potential of the bob at the horizontal position is given as $=m g h=m g \mid$ When the bob goes from the horizontal position to the lowest...
. If the collision is elastic, which of the following figure is a possible result after collision?Solution: The mass of the ball bearing is given as $\mathrm{m}$ Before the collision, Total Kinetic Energy of the system will be $=1 / 2 m v^{2}+0=1 / 2 m v^{2}$ After the collision, Total Kinetic...
and angle 
with the normal, and rebounds with the same speed. Is momentum conserved in the collision? Is the collision elastic or inelastic?For an elastic or inelastic collision, momentum is always preserved. The molecule approaches and rebounds with the same speed of $200 \mathrm{~m} / \mathrm{s}$. $u=v=200 \mathrm{~m}...
, and the second with 
. Which is faster, the electron or the proton? Obtain the ratio of their speeds. (electron mass 
, proton mass 
)Electron mass is given as $m_{e}=9.11 \times 10^{-31} \mathrm{~kg}$ Proton mass is given as $m_{p}=1.67 \times 10^{-27} \mathrm{~kg}$ Electron's kinetic energy can be calculated as...
Power is given by, $P=F V$ $=\operatorname{mav}=\operatorname{mv} \frac{d v}{d t}$ vdv $=\frac{k}{m} \mathrm{dt}$ On integration, we get, 10 $\frac{v^{2}}{2}=\frac{k}{m} d t$...
(a) In an inelastic collision, there will be a loss of kinetic energy. After a collision, the K.E is always lower than the K.E before the impact. In an inelastic collision, the system's total linear...
(a) False. The work done by the conservative force on the moving body in a closed loop is zero. (b) True
(a) External force Internal forces, regardless of their direction, cannot cause a change in momentum. As a result, the change in total momentum is proportional to the system's external force. (b)...
(a) Decreases When a body is displaced in the direction of the force, the conservative force does positive work on it, causing the body to migrate to the center of force. As a result, the distance...
carrying a mass of on his hands. In Fig., he walks the same distance pulling the rope behind him. The rope goes over a pulley, and a mass of hangs at its other end. In which case is the work done greater?Solution: (a) As the satellite approaches the Earth, its potential energy drops, and since the system's total energy should remain constant, the kinetic energy increases. As a result, the...
, where 
is the force constant of the oscillator. For 
, the graph of 
versus is shown in Figure. Show that a particle of total energy 
moving under this potential must ‘turn back’ when it reaches 
.Solution: Energy of the particle will be, $\mathrm{E}=1 \mathrm{~J}$ $\mathrm{K}=0.5 \mathrm{~N} \mathrm{~m}^{-1}$ $\mathrm{K} . \mathrm{E}=\frac{1}{2} \mathrm{mv}^{2}$ Based on law of conservation...
(a) (b) The total energy is given by the relation, $E=K . E .+P . E$. So, $K_{. E}=E-P . E .$ There can never be a negative amount of kinetic energy. In the region where K.E. becomes negative, the...
initially at rest moves under the action of an applied horizontal force of 
on a table with the coefficient of kinetic friction 
Compute the
,.Mass of the body is given as $2 \mathrm{~kg}$ Horizontal force applied is given as $7 \mathrm{~N}$ Coefficient of kinetic friction is given as $0.1$ Acceleration produced by the applied force can be...
Work completed is negative. It is noticed that the bob's orientation and the air resistance acting on it are in different directions.
(a) The direction of motion of the object is opposite the direction of the frictional force, as can be seen. As a result, the work completed is negative. (b) The frictional force acting on an object...
Effective resistance = 1/R + 1/R = 2/R Current, I = V/(R/2) = 0.6A V/R = 0.3A switch is closed, Effective Resistance = Re 1/Re = 1/R + 1/R + 1/R = 3/R Re = R/3 Therefore, final current, I = V/(R/3)...
answer: Total current = I = I1 + I2 + I3 from ohms law I = V/R, I1 = V/R1 I2 = V/R2 I3 = V/R3 V/R = V/R1 + V/R2 + V/R3 1/R = 1/R1 + 1/R2 + 1/R3
Answer: i) Total resistance = R Given, R1 = 5 ohms R2 = 3+2 = 5 ohms 1/R = 1/5 + 1/5 R = 2.5 ohms ii) Current flowing through the circuit, I = V/R = 1.6 amps
Answer: The above circuit shows resistances R1 and R2 connected in series with a battery of V volts Total current = I = I1 + I2 apply ohms law, I=V/R I1 = V/R1 I2 = V/R2 V/R = V/R1 + V/R2 1/R = 1/R1...
c) B can be used in the making of the heating elements of an electric iron because the resistivity of B is the highest . d) C and E are the two substances that should be used for making electric...
Answer: a) E is the best conductor of electricity because it has the least resistivity . b) C is a better conductor between A and C because the resistivity of C is lesser than that of A .
Answer: Effective resistance = R 1/R = 1/R1 + 1/R2 + 1/R3 1/R=1/30 + 1/10 +1/5 R=3 ohm
Answer : c) Insulator is B = 1.0×1010 Ωm . d) Semiconductor is D = 2.3×103 Ωm .
Answer: A parallel circuit is a circuit in which the electricity travels over numerous separate pathways. i) Current through R1=6/5 = 1.2A Current through R2 =6/10= 0.6A Current through R3 =6/30=...
Answer: a) Good conductor is C = 10.0×10-8 Ωm . b) Resistor is A = 110×10-8 Ωm .
Answer: d) one-fourth is the correct answer. We know p=v²/R where R is constant p turns 1/4 times when V is halved The electric power is one-fourth of the actual value when the potential difference...
Show 
Where 
is the momentum of the 
particle (of mass 
and 
Note 
is the velocity of the 
particle with respect to the centre of mass.Also, verify using the definition of the centre of mass that 
Where 
is the total kinetic energy of the system of particles, 
is the total kinetic energy of the system when the particle velocities are taken relative to the center of mass and 
is the kinetic energy of the translation of the system as a whole.i)Here $\vec{r}_{i}=\vec{r}_{i}+\vec{R}+R \ldots$ also, $\vec{V}_{i}=\vec{V}_{i}+\vec{V} \ldots \ldots .$ Where $\vec{r}_{i}^{\overrightarrow{3}}$ and $\vec{v}_{i}^{\overrightarrow{3}}$ denote the...
Answer : c) For making of the solar cells, P = 2.3×103 Ωm can be used because this materials is a semiconductor .
Answer: c) 293 is the correct answer. When all 293 bulbs are linked in parallel and have 75W and 220V, a total of 293 bulbs can be used.
Answer: The resistances R1,R2 and R3 are linked in series with a V volt battery in the circuit above. Let V1 be the potential difference between R1 and V2 be the potential difference between R2....
Answer: a) For making of the electric wires, Q = 2.63×10-8 Ωm can be used because this material has a very low resistivity b) For making of the handle for soldering iron, R = 1.0×1015 Ωm can be used...
Answer: d) 3 J/s is the correct answer. Electrical energy transfered per second , E=VIt=6 x 0.5 x 1 When a light with a voltage of 6V and a current of 0.5A is utilised, 3 J/s of electrical energy is...
Answer: d) 15A is the correct answer. Current drawn by the kettle, I=P/V = 3000/230 So the cable should be able to carry more current than this and hence the answer is 15 A. An electric kettle with...
Answer: d) 6000J is the correct answer. According to the question, Power= 100 W Time, t = 1 minute = 60 seconds P=W/t W=6000J Energy is the ability to do work. Hence, In one minute, 6000J of energy...
Answer: given V=6V, Current through 5 ohm resistor =V/R= 2A i) V = IR R = 3 ohm ii) V = 10 + 6 = 16V
Answer: We know that, R = ρl/A Given that, l’ = 2l A’ = A/2 And ρ’ = ρ (as the material of the wire is the same) Therefore, R’ = ρ’l’/A’ = ρ2l/(A/2) = 4ρl/A = 4R Therefore, R’ = 4×20 =...
Answer: c) Kilowatt-hour is the right answer. The commercial unit of energy is the kilowatt hour.
Answer: a) Joule is the correct answer. The joule is the SI unit of energy.
Answer: The correct option is b) 2 times. Reason: As, R = ρl/A so R' = ρl/(A/2) = 2ρl/A ⇒R' = 2R So , new resistance becomes 2 times the original resistance .
Answer: i) Current through 5 ohm resistor =V/R= 2A ii) Current through R = 2A because 5 ohm resistor and R are connected in series
(a) False. The instantaneous acceleration of a rolling object will have a value that is not zero. (b) True. Because the frictional force is zero during perfect rolling, no work is done against it.
Answer: b) Rupees 24 is the correct answer. It is assumed that the cost of electrical energy is rupees 4 per kWh. The duration of the event is 3 hours. The electric heater has a 2kW output. We can...
Answer: b) 850W is the proper option. The electric irons we use in our homes have a power rating of 850W.
and radius 
is rolling perfectly on a plane of inclination 
The coefficient of static friction 
. If the inclination 
of the plane is increased, at what value of does the cylinder begin to skid, and not roll perfectly?The given situation can be depicted as: Mass is given as $m=10 \mathrm{~kg}$ Radius is given as $r=15 \mathrm{~cm}=0.15 \mathrm{~m}$ Co-efficient of kinetic friction is given as $\mu_{s}=0.25$ Angle...
Answer: d) Watt is the correct answer. The watt is the unit of measurement for electric power.
Answer: b) 6W is the correct option P = VI is the formula for calculating power Substituting the values of V and I, we get P = 6W.
Answer: The resistances R1 and R2 are linked in series with a V volt battery in the circuit above. Let V1 be the potential difference between R1 and V2 be the potential difference between R2. ...
Answer: The correct option is c) Temperature . Reason : The resistivity or specific resistance of a material is an intensive property (property which does not depend on the system size or the amount...
Answer: c) One kilowatt hour is the amount of energy utilised by an electrical equipment with a power of one kilowatt for one hour. d) Given in the question, P = 500W = 0.5kW T = 20 hour Thus,...
are placed on a horizontal table simultaneously, with an initial angular speed equal to 
. Which of the two will start to roll earlier? The coefficient of kinetic friction is 
The radius of the ring and the disc is given as r = 10 cm = 0.10 m Initial angular speed is given as ω0 =10 π rad s–1 The coefficient of kinetic friction is given as μk = 0.2 According to Newton’s...
Answer: The correct option is b) half Reason: Resistance is inversaly proportional to (A) Area (cross sectionsl area of conductor) . R∝ 1/A So when A Doubled then Resistance became half .
Answer: Total current flowing through circuit, I = 6A R1 = 3 Ω R2 = 6 Ω Combined resistance R is 1/R = 1/3 + 1/6 = 3/6 R = 2 Ω Potential difference across the combined resistance = IR = 12V...
Answer: Total current flowing through circuit, I = 6A R1 = 3 Ω R2 = 6 Ω Combined resistance R is 1/R = 1/3 + 1/6 = 3/6 R = 2 Ω Potential difference across the combined resistance = IR = 12V a)...
Answer: a) The rate at which electrical energy is consumed is referred to as electric power. It is given as: P = VI = watt b) Given in the question, V =...
Answer: The correct option is d) A semiconductor . Reason : The resistivity of a certain material is 0.6 Ωm. The material is most likely to be a semiconductor because it has moderate...
is placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is R. What are the linear velocities of the points 
and 
on the disc shown in Figure. Will the disc roll in the direction indicated?Solution: The respective linear velocities are : For point $A, v_{A}=r \omega_{0}$ For point $B, v_{B}=r \omega_{0}$ both in the direction of arrow For point $C, v_{c}=(R / 2) \omega_{0}$ in the...
answer: Given that Total current flowing through circuit, I = 6A R1 = 3 Ω R2 = 6 Ω a) Combined resistance R is 1/R = 1/3 + 1/6 = 3/6 R = 2 Ω b) Potential difference across the combined resistance =...
Answer: The correct option is a) four times. Reason : Resistance of the wire is given by: R = ρ lA When the diameter is halved: d'=d2 Radius: r'=r2 Area of cross-section: A'=πr'2=πr22=πr24=A4 Area...
in the 
plane from an axis through the origin and perpendicular to the plane is 
.
.(a) The moment of inertia of a planar body (lamina) about an axis perpendicular to its plane is equal to the sum of the moments of inertia of the lamina about any two mutually perpendicular axes in...
Effective resistance = R1+R2=20 + 20 = 40 ohms a) Current flowing through the circuit = I = V/R = 5/40 = 0.125amp b) Potential difference across each resistance = IR = 2.5V
Answer: a) b) Effective resistance = R1+R2=20 + 20 = 40 ohms
Answer: Given in the question, V = 230V I = 0.4amp We have to find the rate at which electrical energy is transferred i.e., Power We know that, P = VI Substituting the values of V & I, we get P...
Answer: Given, V = 6V R1 = 2Ω R2 = 3 Ω Effective resistance = R 1/R = ½ + 1/3 1/R = 5/6 R = 1.2 Ω Current flowing through battery, I = V/R = 6/1.2 = 5A
Answer: Given in the question, I = 13amp V = 230V We know that, P = VI Substituting the values of V & I, we get P = 2.99kW
answer: Given, V = 6V R1 = 2Ω R2 = 3 Ω a)Because of its lower resistance, 2 ohm resistance has a larger share of current. b) Effective resistance = R 1/R = ½ + 1/3 1/R = 5/6 R = 1.2...
Answer: The correct option is c) 60 Ω. Reason : If the resistance of a certain copper wire is 1 Ω, the resistance of a similar nichrome wire will be about 60 Ω because the resistivity of nichrome is...
Answer: Given, V = 6V R1 = 2Ω R2 = 3 Ω a) Resistors are connected in parallel b) The potential difference across each resistor is equivalent to...
Answer: In parallel, 4 and 2 coils are connected. As a result, the total resistance, R 1/R = ¼ + ½ = ¾ R = ¾ Ω Total current,, I = V/R = 3 Ω V/(4/3) = 3...
Answer: The correct option is d) 30Ω Reason : We know that R = ρl/A Substituting the values in the above equation we get 30Ω.
Answer: d) 7 (1/2) is the correct answer. When combining resistors, the series and parallel combination formula must be employed. A parallel combination of 6 and 2 resistors is used....
Answer: The correct option is d) one-fourth Reason: We know that R = ρl/A Therefore, when the diameter of the wire is doubled, the resistance becomes one-fourth of the actual value.
and speed 
is fired into a door and gets embedded exactly at the centre of the door. The door is 
wide and weighs 
. It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it.Velocity is given as v = 500 m/s Mass of bullet is given as m = 10 g or 10 × 10–3 kg The width of the door is given as L = 1 m The radius of the door is given as r = 1 / 2 Mass of the door is given...
Answer: It is given for heater, P = 2kWh T = 4 hours Thus, Energy consumed will be E1, PT = 8kWh It is given for TV, P = 200 watt = 0.2kW T = 4 hours Thus, Energy consumed will be E2, PT = 0.8kWh...
Answer: c) 20 is the correct answer. The overall resistance acquired is equivalent to 20 since the resulting resistance generated from the resistors that are connected in series is connected with 40...
Answer: The correct option is d) 30Ω We know that R = ρl/A Substituting the values in the above equation we get 30Ω.
Answer: a) 9 is the correct answer. The overall resistance of the supplied circuit is calculated using a series and parallel combination once more.
e) Given in question : l = 1m , R = 26Ω r = d/2 = 0.3/2 = 0.15mm = 0.15×10-3m We know that, ρ = R×A/l ρ= 1.83×10-6Ωm .
c) Following are the differences between resistance and resistivity: Resistance is the property of the conductor whereas Resistivity is the property of the material used in the conductor . In a...
Answer: c) 1V is the correct answer. We know that V = IR equals the potential difference across a resistor. As a result of swapping the values, we get a potential difference of 3V across the...
long and hinged at A. A rope DE, 
m is tied halfway up. A weight 
is suspended from a point F, 
from B along with the ladder BA. Assuming the floor to be frictionless and neglecting the weight of the ladder, find the tension in the rope and forces exerted by the floor on the ladder. (Take 
) (Hint: Consider the equilibrium of each side of the ladder separately.)Solution: The above figure can be redrawn as, where, $N_{B}$ is the force being applied by floor point $B$ on the ladder $N_{c}$ is the force being applied by floor point $C$ on the ladder The...
Answer: b) The current at Y is greater than the current at Z is the correct answer
Answer: Given in the question, V = 230V I = 10amp a) We know that, P = VI Substituting the values of V & I, we get P = 2300 watt = 2300 J/s b) Also, energy consumed in one minute = PT = 138000...
Answer: Where V1 = 5.0, V2 = 10.0, and V3 = 15.0 is the correct answer. We can acquire the correct numbers for V1, V2, and V3 by using the formula V = IR and replacing the values in the...
Answer: a) Resistivity is defined as: ρ = R×A/l where,R is the resistance of the conductor, A is the cross-sectional area of the conductor and l is the length of the conductor. b) The SI unit of...
Answer: c) The amount of energy consumed by 40W lamp in 1 hour, E1 = PT = 40 watt-hour 1 watt-hour = 3.6kj Thus, E1 = 144kJ Energy consumed by 60 watt lamp in 1 hour, E2 = PT = 216kJ Total energy...
Answer: Given in question , l = 1.0m , R = 23 ohm , ρ = 1.84×10-6Ωm We have, R = ρl/A 23 = 1.84×10-6 × 1/A A = 8×10-8 m2
Answer: d) 25 is the correct answer. The ratio of the resistance and the resulting resistance achieved when the parts are linked in parallel is 25 when a resistance wire is cut into...
c) ρ = 3ρ R’ = 3ρl/A = 3R Therefore, resistance becomes 3 times.
Answer: We know that, R = ρl/A a) l becomes 3l R’ = ρ3l/A = 3R Therefore, resistance gets tripled b) d becomes 3d & R = ρl/A R = ρl/πr2 = ρl/π(d/2)2 R’ = R/9 Therefore, resistance becomes...
Answer: a) When a wire's resistance is changed, the cross-sectional area increases, lowering the resistance. b) When a wire's resistance is changed, the material's diameter is increased, lowering...
Answer: c) As the temperature is increased, the resistance will increase
Answer: Given in the question, Number of lamps = 2 P1 = 40W P2 = 60W V = 220V a) Circuit diagram is shown below, b) The voltage across both bulbs is the...
Answer: The following are the impacts on a metal wire's resistance when: a) The resistance will grow when the length is increased. As $R=\rho L/a$ i.e resistance is directly proportional to length...
At the bottom of the inclined plane, the centre of mass of the cylinder has a speed of 
.initial velocity of the solid cylinder is given $v=5 \mathrm{~m} / \mathrm{s}$ Angle of inclination is given as $\theta=30^{\circ}$ We assume that the cylinder goes up to a height of $h$, so we get:...
and a moment of inertia of 
about an axis through its centre perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is 
and that its kinetic energy of rotation is two-thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.Mass of one oxygen molecule is given as $m=5.30\times10^{-26}kg$ So, the mass of each oxygen atom will be $\frac{m}{2}$ Moment of inertia is given as $I=1.94\times10^{-46}kg m^{2}$ Velocity of the...
Answer: Given, V = 6V R1 = 2 Ω R2 = 3 Ω Combined resistance, Rt = 2+3 = 5 Ω I = V/Rt = 10/5 = 2A a) Potential difference across 2 Ω resistor = IR1 = 4V b) Potential difference across 3 Ω resistor =...
Answer: Given, V = 6V R1 = 2 Ω R2 = 3 Ω a) resistance of combination , Rt = 2+3 = 5 Ω b) Current flowing I = V/Rt = 10/5 = 2A
Answer: Given, V = 6V R1 = 3 Ω R2 = 6 Ω Current via three resistors = V/R1 = 6/3 = 2A
Answer: Given, V = 6V R1 = 3 Ω R2 = 6 Ω a) Resistance in combination, 1/R = 1/R1 + 1/R2 = 1/3 + 1/6 = ½ R2 = 2 b) Current flowing in the main...
Answer: Given, V = 4V R1 = 6 Ω R2 = 2 Ω Combined resistance, R = R1 + R2 = 8 ohm Current flowing, I = V/R = 4/8 = 0.5 amp Difference in potential...
Answer: Given, V = 4V R1 = 6 Ω R2 = 2 Ω a) Combined resistance, R = R1 + R2 = 8 ohm b) Current flowing, I = V/R = 4/8 = 0.5 amp ...
Answer: a) Given in the question, V = 6V R1 = 1 ohm R2 = 2 ohm Thus, we get Equivalent resistance of R1 & R2 in series, R = R1 + R2 = 3 ohm Total current, I = V/R = 6/3 = 2amp Current through...
Answer: Given, V = 12V R1, R2, and R3 are linked in a series. Current through R1 = V/R1 = 12/5 = 2.4 A Current through R2 = V/R2 = 12/10 = 1.2 A Current through R3 = V/R3 =...
Answer: 1st case: TV set Given, P = 250W = 0.25kWh T = 1 hour Thus, we get Energy consumed, E = PT = 0.25kWh 2nd case: Toaster Given, P = 1200W = 1.2kW T = 10 min = 1/6 hour Thus, we get Energy...
Given, V = 12V R1, R2, and R3 are linked in a series. a) Current through R1 = V/R1 = 12/5 = 2.4 A Current through R2 = V/R2 = 12/10 = 1.2 A Current through R3 =...
Answer: Given in the question, I = 5amp V = 220V T = 2 hours We have to find P = ? E = ? We know that, P = VI Substituting the values of V & I, we get P = 1.1kW Also we know that, Energy...
Answer: a) R1 represents the equivalent resistance of 10 and 40 resistances: 1/R1 = 1/10 + 1/40 = 5/40 R1 = 8 Ω R2 is the equivalent resistance of 30 ohms, 20...
Answer: Given in the question that, P = 4kW V = 220V T = 2hours c) Energy consumed in two hours, E = PT Substituting the values of P & T, we get E = 8kWh d) Cost of 1kWh = Rupees 4.6 Total cost...
(a) Let m be the mass of the ball let h be the height of the ball let v be the final velocity of the ball at the bottom of the plane The ball possesses Potential energy $mgh$ at the top of the...
When coils A and B are utilised in parallel, the current drawn is: Total resistance is 1/R = 1/Ra + 1/Rb = 1/24 + 1/24 = 2/24 = 1/12 R = 12 ohms I = V/R = 220/12 = 18.33 amps
answer: given Ra = Rb = 24 ohm a) Current drawn when coil A is the only one used: I = V/Ra = 220/24 = 9.16 amps b) Current drawn in series when coils A and B are used: Total resistance, R = Ra + Rb...
Answer: given that I = 5 amp V = 220 V R = V/I = 220/5 = 44 ohm The resultant resistance must be less than 176 ohm. Therefore, the resistors are connected in parallel Let...
Answer: Given in the question that, P = 4kW V = 220V a) Current, I = ? We know that, P = VI Substituting the values of P & V, we get I = 16amp b) Resistance, R = ? We know that, P = I2R...
Given, 1 amp = I R = 5 ohm ohm ohm ohm o Because the resistors are linked in parallel and the voltage across them is the same, the potential difference across each resistor is the same....
V/R = total current flowing through circuit Where R stands for total resistance. I = 12/6 = 2 amp Difference in potential across R1 = R1I = 8V
Answer: It is given in the question that, V = 250V I = 0.4 amp a) We have to find P = ? We know that, P = VI Substituting the values of V & I, we get P = 100 watt b) We have to find R = ? We...
answer: When two resistors are linked in parallel, the total resistance is 1/3 + 1/6 = 1/R' 3/6 = 1/R' R' is equal to 2 ohms. Total circuit resistance = 2 + 4 = 6...
Answer: 1st case, Power, P1 = 60W Number, n1 = 2 Time for use, T1 = 4 hours everyday Energy consumed, E1 = n1 × P1 × T1 E1 = 2 × 60 × 4 = 480watt-hour = 0.48kWh As a result, total energy consumed...
answer: a) When the two resistors are linked in series, the current through the resistors is kept to a minimum. The current flow is greatest when the resistors are linked in parallel. b) If the...
a) The relation between electric charge, time, and electric current is given as: Current $=($charge moved$) /($time$)$ While work done = potential difference $\times$ charge moved Therefore, above...
answer: Assume the following circuit: V = 4V Total resistance in line 1 = R1 = 6 + 3 = 9 Ω Total resistance in line 2 = R2 = 12 + 3 = 15 Ω a) Current flowing...
Answer: It is given in the question that, V = 220V P = 2.2kW = 2200 watt T = 3 hours It is known to us that Energy consumed = PT = 6.6kWh We also know that, P = VI Thus we get, I = 10...
As we all know, resistance is the measurement of an electrical circuit's resistance to current flow. The current is measured with an ammeter, while the potential difference is measured with a...
A device used to measure the flow of electric current is known as an ammeter. An ammeter is always linked in series with the electric current being measured. The following diagram shows how to...
a) An electric current is defined as the flow of electric charges through a conductor where the flow of current is caused by the potential difference between two locations in the conductor. b) The...
a) A cell or a battery is used to sustain the potential difference across a conductor. b) Given, Potential difference $=10 \mathrm{~V}$, Current, I $=2 \mathrm{~A}$ Time taken, $t=60 \mathrm{~s}$ We...
Answer: a) It is given in the question that, R = 300 ohm I = 1 amp T = 1 hour P = I2R = 300W E = PT = 300 watt-hour b) It is given in the question that, R = 100 ohm I = 2 amp T = 1 hour P = I2R =...
a) Electrons and closed b) Amperes, ammeter, and series
Given, Time taken, $t=10 s$ Charge moved, $\mathrm{Q}=25 \mathrm{C}$ Energy delivered is work done $=200 \mathrm{~J}$ a) Potential difference $=($ work done $) /($ charge moved $)=(200) /(25)=8...
Answer: It is given in the question that, V = 220V I = 0.5A P = ? It is known to us that, P = VI P = 110 watt
Answer: a) To brighten the lights, turn the switch to the right, as the resistance lowers as the switch is turned to the right. As a result, the circuit's resistance will be reduced. b) To dim the...
Given, Potential difference $=12 \mathrm{~V}$ a) Potential difference = (work done)/(charge moved) Work done = Potential difference$\times$ charge moved Therefore, $12 \mathrm{~J}$ of electrical...
Answer: a) When the lamps are connected in a series, the lamps will stop lighting if one of the filaments breaks. Because the circuit is broken due to the broken lamp. b) When the lamps are...
Answer: When two bulbs are linked in parallel instead of series, they create more light. This occurs because the voltage difference between parallel combinations remains constant. However, in the...
Answer: c) B and A are connected in series. If B burns out, A will also burn out. C, on the other hand, remains the brightest as it is in parallel combination with the other two.
Given, Charge moved $=1.6 \times 10^{-19}$ coulombs Current, I $=1 \mathrm{~A}$ Time taken, $t=1 \mathrm{~s}$ We know that, $\text{I}=\text{Q}/\text{t}$ $1=\text{Q}/1$ $\text{Q}=1\text{C}$ We also...
A circuit diagram is a graphic that uses electric symbols to show the individual components in an electric circuit and how they are connected. A voltmeter, on the other hand, will have a higher...
a) Because the value of the current flowing through the circuit is constant, the resistance of an ammeter should be very low. b) A voltmeter's resistance should be quite high since the current...
c) Voltage is another word for potential difference.
The correct answer is a) An ammeter is connected in series in a circuit and a voltmeter is connected in paralle
Answer: a) Let us consider two wires with same length and diameter. Let these two wires be of copper metal and nichrome alloy. We know that the resistance of nichrome wire is 60 times more than...