Which of the following potential energy curves in Fig. 6.18 cannot possibly describe the elastic collision of two billiard balls? Here r is the distance between centres of the balls.

A person of mass 60 kg wants to lose 5kg by going up and down a 10m 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 kilo calories, how many times must he go up and down to reduce his weight by 5 kg?

On complete combustion a litre of petrol gives off heat equivalent to 3×10⁷ J. In a test drive a car weighing 1200 kg. including the mass of driver, runs 15 km per litre while moving with a uniform speed on a straight track. Assuming that friction offered by the road surface and air to be uniform, calculate the force of friction acting on the car during the test drive, if the efficiency of the car engine were 0.5.

A bob of mass m suspended by a light string of length L is whirled into a vertical circle as shown in Fig. 6.11. What will be the trajectory of the particle if the string is cut at

(a) Point B?

(b) Point C?

(c) Point X?

Give example of a situation in which an applied force does not result in a change in kinetic energy.

Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in contact (Fig. 6.14). One of the bobs is released after being displaced by 10⁰ so that it collides elastically head-on with the other bob.

(a) Describe the motion of two bobs.

(b) Draw a graph showing variation in energy of either pendulum with time, for 0 ≤ t ≤ 2T, where T is the period of each pendulum.

Figure (8-E4) shows a particle sliding on a frictionless track which terminates in a straight horizontal section. If the particle starts slipping from the point A, how far away from the track will the particle hit the ground?

A body is falling freely under the action of gravity alone in vacuum. Which of the following quantities remain constant during the fall?

Suppose the average mass of raindrops is 3.0 × 10^-5 kg and their average terminal velocity 9 m

s^-1. Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year.