First slide

Types of collision

Question

A ball of mass m moving with a certain velocity collides against a stationary ball of mass m. The two balls stick together during collision. If E be the initial kinetic energy, then the loss of kinetic energy in the collision is

Moderate

A

E
B

E/2
C

E/3
D

E/4

Solution

Applying the law of conservation of momentum
${mv}_{1} + 0 = (2 m) v_{2} . . v_{2} = (v_{1} / 2) Loss of K.E. = \frac{1}{2} {mv}_{1}^{2} - \frac{1}{2} (2 m) {v_{2}}^{2} = \frac{1}{2} {mv}_{1}^{2} - \frac{1}{2} \times 2 m \times (v_{1}^{2} / 4) = \frac{1}{2} {mv}_{1}^{2} (1 - \frac{1}{2}) = E / 2$

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