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Question

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.

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Solution

Given that

For the case of elastic collision of two billiard balls, the potential energy is inversely dependent on the distance between them. Thus, when the balls are moved apart, the potential energy increases and when it is moved close to each other, the potential energy decreases.

The value of potential energy will become

In graph (i), the value of

In graph (ii), the value of

In graph (iii), the value of

Graph (iv) shows negative potential energy after

Graph (v) satisfies both the given conditions for the case of elastic collision.

In graph (v), the value of

Hence, potential energy curves (i), (ii), (iii), (iv) and (vi) cannot possibly describe the elastic collision of two billiard balls.

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