Answer : According to the question, the surface tension of the soap solution is S = 2.50 × 10-2 N/m r = 5.00 mm = 5 × 10-3 m We know that the density of the soap solution is ρ = 1.2 × 103 kg/m3 and...
What is the excess pressure inside a bubble of soap solution of radius 5.00 mm, given that the surface tension of soap solution at the temperature (20 °C) is 2.50 × 10–2 N m–1 ? If an air bubble of the same dimension were formed at depth of 40.0 cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble ? (1 atmospheric pressure is 1.01 × 105 Pa)
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. 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?
, and that of the 
wave is 
. A seismograph records 
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?
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 
.
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.
, (that is the whistle is blown for a split of second after every 
or 
?
, and 
? Is this velocity equal to the velocity of wave propagation?
and 
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 
.
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 
, find the frequency of 
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 
).
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?
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.
. The linear mass density of the string is 
m and its mass is 
kg. Calculate:
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:
away from one end?
and its length is 
. 
. What is the phase difference between the oscillatory motion of two points separated by a distance of:
, 
and ![]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-478d84af1027ee3593251b323a3fb181_l3.png "Rendered by QuickLaTeX.com")
.
,
plot the displacement ( 
0,2 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")
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.
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 
represents a wave travelling in one direction, where 
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")
explain why the speed of sound in air increases with humidity.
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 
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 
J of work per minute and services 
J of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per minute?
of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure? (Molecular mass of 
.)
co-exist in equilibrium? (b) What is the effect of the decrease of pressure on the fusion and boiling point of 
and thickness 1.0 cm. It boils water at the rate of 6.0 kg/min when placed on a gas stove. Estimate the temperature of the part of the flame in contact with the boiler. Thermal conductivity of brass = 
; Heat of vaporisation of water = 2256 × 103 
.
. [Heat of fusion of water = 335 × 103 
. What is the fractional change in its density for a 30 °C rise in temperature?
.
.
.
is related to the temperature tc on the Celsius scale by tc = T – 273.15. Why do we have 
in this relation, and not 273.16? (d) What is the temperature of the triple-point of water on an absolute scale whose unit interval size is equal to that of the Fahrenheit scale?
and 
, respectively. On the absolute scale, one of the fixed points is the triple-point of water, which on the Kelvin absolute scale is assigned the number 
What is the other fixed point on this (Kelvin) scale?![\mathbf{R}=\mathbf{R}_{\mathrm{o}}\left[1+\alpha\left(\mathrm{T}-\mathrm{T}_{0}\right)\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7d41138edf78cb4422493eb359a7f99c_l3.png "Rendered by QuickLaTeX.com")
The resistance is 
at the triple-point of water 
, and 
at the normal melting point of lead (600.5 K). What is the temperature when the resistance is 
?
and 
. What is the relation between TA and TB?
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?
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.
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?
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.
and cross-sectional area 
is stretched, well within its elastic limit, horizontally between two pillars. A mass of 
is suspended from the mid-point of the wire. Calculate the depression at the midpoint.
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.
?
on an edge, when subjected to a hydraulic pressure of 
.
atm, given that its density at the surface is 
?
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.
mass, fastened to the end of a steel wire of unstretched length 
at the bottom of the circle. The crosssectional area of the wire is 
Calculate the elongation of the wire when the mass is at the lowest point of its path.
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.
supports a chairlift at a ski area. If the maximum stress is not to exceed 
What is the maximum load the cable can support?
. 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.
is then attached to the opposite face of the cube. The shear modulus of aluminium is 
. What is the vertical deflection of this face?
, 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")
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?
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.
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?
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 
, 
, and 
, what are the speeds and times taken by the two stones?
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.
of power. (a) Direct solar energy is incident on the horizontal surface at an average rate of 
per square meter. If 
of this energy can be converted to useful electrical energy, how large an area is needed to supply 8 kW?(b) Compare this area to that of the roof of a typical house.
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 
of the wind energy is converted into electrical energy and 
and the density of the air is 
What is the electrical power produced?
travels in a straight line with velocity 
where 
. What is the work done by the net force during its displacement from 
m?
carrying a sandbag of 
is moving uniformly with a speed of 
on a frictionless track. After a while, the sand starts leaking out of a hole on the floor of the trolley at the rate of 
What is the speed of the trolley after the entire sandbag is empty?
of its initial energy against air resistance?
to the vertical is released and it hits a ball B of same mass which is at rest. Does the ball A rises after collision? The collision is an elastic collision.
. If the collision is elastic, which of the following figure is a possible result after collision?
in 
. If the tank is 
above the ground, and the efficiency of the pump is 
, how much electric power is consumed by the pump?
and angle 
falls from a height of 
above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height, it attains its maximum (terminal) speed, and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey? What is the work done by the resistive force in the entire journey if its speed on reaching the ground is 
?
, and the second with 
. Which is faster, the electron or the proton? Obtain the ratio of their speeds. (electron mass 
, proton mass 
)
given by 
where i, 
, are unit vectors along the 
– and 
-axis of the system respectively. What is the work done by this force in moving the body at a distance of 
along the z-axis?
carrying a mass of 
, where 
is the force constant of the oscillator. For 
, the graph of 
versus 
moving under this potential must ‘turn back’ when it reaches 
.
initially at rest moves under the action of an applied horizontal force of 
on a table with the coefficient of kinetic friction 
Compute the
,
where 
is the angular momentum of the system about the centre of mass with velocities considered with respect to the centre of mass. Note 
, rest of the notation is the standard notation used in the lesson. Note L’ and MR 
can be said to be angular momenta, respectively, about and of the centre of mass of the system of particles.
Further prove that: 
Where t’ext is the sum of all external torques acting on the system about the centre of mass. (Clue : A pply Newton’s Third Law and the definition of centre of mass. Consider that internal forces between any two particles act along the line connecting the particles.)
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.
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 
. Which of the two will start to roll earlier? The coefficient of kinetic friction is 
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?
is given by 
using dynamical consideration (i.e. by consideration of forces and torques). Note 
is the radius of gyration of the body about its symmetry axis, and 
is the radius of the body. The body starts from rest at the top of the plane.
in the 
plane from an axis through the origin and perpendicular to the plane is 
.
.
and 
about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds 
and 
are brought into contact face to face with their axes of rotation coincident.
and speed 
is fired into a door and gets embedded exactly at the centre of the door. The door is 
. 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.
weight in each hand. The angular speed of the platform is 30 revolutions per minute. The man then brings his arms close to his body with the distance of each weight from the axis changing from 
to 
. The moment of inertia of the man together with the platform may be taken to be constant and equal to 
.
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.)
.
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.
How much work has to be done to stop it?