Physic

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1 A block of mass 100 g is moved with a speed of 5.0 m/s at the highest point in a closed circular tube of radius 10 cm kept in avertical plane. The cross-section of the tube is such that the block just fits in it. The block makes several oscillations inside thetube and finally stops at the lowest point. Find the work done by the tube on the block during the process.

2 A car weighing 1400 kg is moving at a speed of 54 km/h up a hill when the motor stops. If it is just able to reach the destinationwhich is at a height of 10 m above the point, calculate the work done against friction (negative of the work done by the friction).

3 A turn of radius 20 m is banked for the vehicles going at a sped of 36 km/h. If the coefficient of static friction between the roadand the tyre is 0.4, what are the possible speeds of a vehicle so that it neither slips down nor skids up ?

4 A chain of length l and mass m lies on the surface of a smooth sphere of radius R > l with one end tied to the top of the sphere.(a) Find the gravitational potential energy of the chain with reference level at the centre of the sphere, (b) Suppose the chain isreleased and slides down the sphere. Find the kinetic energy of the chain, when it has slid through an angle . (c) Find the

tangential acceleration dtdv

of the chain when the chain starts sliding down.

5 A scooter weighing 150 kg together with its rider moving at 36 km/hr is to take a turn of radius 30 m. What horizontal force onthe scooter is needed to make that turn possible ?

6 Suppose the amplitude of a simple pendulum having a bob of mass m is 0. Find the tension in the string when the bob is atits extreme position.

7 A motorcycle has to move with a constant speed on an overbridge which is in the form of a circular arc of radius R and has atotal length L. Suppose the motorcycle starts from the highest point. (a) What can its maximum velocity be for which the contactwith the road is not broken at the highest point ? (b) If the motorcycle goes at speed 2/1 times the maximum found in part (a),where will it lose the contact with the road ? (c) What maximum uniform speed can it maintain on the bridge if it does not losecontact anywhere on the bridge ?

8 Water falling from a 50 m high fall is to be used for generating electric energy. If 1.8 × 105 kg of water fallsl per hour and halfthe gravitational potential energy can be converted into electric energy, how many 100 W lamps can be lit ?

9 A person is painting his house walls. He stands on a ladder with a bucket containing paint in one hand and a brush in other.Suddenly the bucket slips from his hand and falls down on the floor. If the bucket with the paint had a mass of 6.0 kg and wasat a height of 2.0 m at the time it slipped, how much gravitational potential energy is lost together with the paint ?

10 A block of mass m is kept on a horizontal ruler. The friction coefficient between the ruler and the block is µ. The ruler is fixedat one end and the block is at a distance L from the fixed end. The ruler is rotated about the fixed end in the horizontal planethrough the fixed end. (a) What can the maximum angular speed be for which the block does not slip ? (b) If the angular speedof the ruler is uniformly increased from zero at an angular acceleration , at what angular speed will the block slip ?

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ASSIGNMENT-1CIRCULAR MOTION

ANSWER KEYASSIGNMENT - 1

1 [– 1.45 J] 2 [20300 J] 3 [Between 14.7 km/h and 54 km/hr]

4 [(a) l

gmR2

sin (l/R) (b) l

gmR2

Rl

Rl sinsinsin (c) l

Rg [1– cos (l/R)]] 5 [500 N] 6 [mg cos0]

7 [(a) Rg , (b) a distance R/3 along the bridge from the highest point, (c) )2/cos( RLgR ]

8 [122] 9 [118 J] 10 [(a) Lg / (b) 4/1

22

Lg

]