1. Attempt any two parts:

A ball of mass 0.3 kg moving with a speed of 6.0 ms^­1 strikes a wall at an angle of 60° to the wall. It then rebounds at the same speed and the same angle. It is in contact with the wall for 10 ms. Calculate the impulse and the average force.

A particle's kinetic energy decreases when an external force is exerted on it. Is the force conservative or non-conservative? Explain.

A rock of mass 500 kg slides down from rest along a hill slope that is 500 m long and 300 m high and reaches the bottom. The coefficient of kinetic friction between the rock and the hill slope is 0.25. Calculate

the potential energy of the rock just before sliding.

the work done on the rock by the frictional force.

the speed of the rock at the bottom of the hill. Draw the free body diagram.(Take g 10

A crane operated by an electric motor has a mass of 500 kg. It raises a load of 300 kg vertically at a steady speed of 0.2 ms^-1. The frictional force is constant and equal to 1200 N. Calculate what is the power required. (Take g 10

Suppose a frame of reference is attached to a ball being swung in a circle. Is the frame of reference inertial or non-inertial? Explain.

A wheel has a moment of inertia of 2.0 kg m^2 about its axis of rotation. It is rotating with an angular speed of 50 rpm. Calculate the torque that can stop the wheel in one minute. Also, calculate the work done by the torque in this time.

2. Attempt anyone part:

What are the constants of motion for a particle moving under a central conservative force?

Io and Europa are the moons of Jupiter. 10 takes 1.8 days to orbit Jupiter and it is at a distance of 4.22 x 10^5 km from its centre. Europa is at a distance of 6.71 x 10^5 km from Jupiter's centre. Use Kepler's third law to determine how long it would take Europa to orbit Jupiter.

Write down the expression for the position vector of the centre of mass for a two-particle system. Write the equation of motion for the centre of mass coordinate of a two-particle system if the net external force on it is zero. Two skaters stand on ice holding a pole of length 10 m and negligible mass between them. Their masses are 60 kg and 40 kg. Starting from the ends of the pole the skaters move along the pole till they meet. How far does each skater move?

3. An object is being rotated in a centrifuge of radius 5.0 m. The acceleration of the centrifuge is 4 g. What is the velocity of the object and the time period of its motion (Take g 10

OR

An iceberg of mass 5 x 10^8 kg near the North Pole moves west at a speed of 8 km per day. Determine the magnitude and direction of the Coriolis force.

Derive the expression of the kinetic energy of a two-particle system in terms of the centre of mass and relative coordinates given by

K 1/2 MVcm^2 1/2 mv^2

OR

A body of radius R and mass M is initially rolling on a level surface with speed u. It then rolls up an incline and is able to reach a height where h What is the geometrical shape of the body?

1. Answer any three parts

Explain the phenomenon of beats. An ambulance blowing a siren of frequency 700 Hz is travelling towards a vertical reflecting wall with a speed 7.2 km Calculate the number of beats heard in one second by the driver of the ambulance. Take speed of sound as 340 ms^-1.

An open pipe is suddenly closed at one end with the result that the frequency of the third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. Calculate the fundamental frequency of the open pipe.

An object of mass m is subjected to a restoring force kx and frictional force dx/dy. It oscillates harmonically with a frequency
0.5 Hz. However, its amplitude of oscillation is halved in 2 s and the system is weakly damped. Calculate the values of wd, b and k. Also write down its equation of motion in terms of calculated values.

How is a compound pendulum different from a simple pendulum? Obtain an expression for the time period of a compound pendulum.

Consider two identical spring-mass systems connected by a spring of spring constant

Depict their equilibrium and instantaneous configurations.

Write down the equations of motion of these masses when they are made to execute longitudinal oscillations.

Reduce these equations to the standard equation of SHM and interpret your results.

2. Answer any two parts:

Two waves travelling in the same direction are represented as

a sin (w1t k1x)

and sin (w2t -k2x

Suppose that w1 and k1 are respectively greater than w2 and k2. Obtain an expression for the resultant wave arising due to their superposition.

Consider a body of mass 0.2 kg suspended from a spring of force constant 100 Nm^-1. The frictional force acting on it is 5 v newton. Write down the differential equation of its motion and calculate the period of oscillations.

The group velocity and phase velocity are connected through the relation

vg vp k dvp/dk

Express vg in terms of A.