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

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Solution

The potential energy of a system of two masses is inversely proportional to the separation between them. In the given case, the potential energy of the system of the two balls will decrease as they come closer to each other. It will become zero (i.e., V(r) = 0) when the two balls touch each other, i.e., at r = 2R, where Ris the radius of each billiard ball. The potential energy curves given in figures (i), (ii), (iii), (iv), and (vi) do not satisfy these two conditions. Hence, they do not describe the elastic collisions between them.

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Similar questions

Q. 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.

Answer carefully, with reasons:

(a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact)?

(b) Is the total linear momentum conserved during the short time of an elastic collision of two balls?

(d) If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic? (Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).

Answer carefully, with reasons :

(a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact) ?

(b) Is the total linear momentum conserved during the short time of an elastic collision of two balls ?

Q. In an elastic collision of two billiard balls, which of the following quantities remain conserved during the short time of collision of the balls (i.e., when they are in contact)?

Q. Assertion: In an elastic collision of two billiard balls, the total kinetic energy is conserved during the short time of oscillation of the balls (i.e., when they are in contact).
Reason: Energy spent against friction does not follow the law of conservation of energy.

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

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