First slide

The steps in collision

Question

An object of 2.0 kg mass makes an elastic collision with another object of mass M at rest and continues to move in the original direction but with one-fourth of its original speed. What is the value of M ?

Moderate

A

0.75 kg
B

1.0 kg
C

1.2 kg
D

none of these

Solution

This is a case of head-on elastic collision
$v_{2} - v_{1} = u_{1} - u_{2} \Rightarrow v_{2} - \frac{u}{4} = u - 0 . . . . . . . . . . . . . (1) C o n s e r v i n g m o m e n t u m$
$2 \cdot 0 \times u + M \times 0 = 2 \times \frac{u}{4} + M \times v_{2} \Rightarrow v_{2} = \frac{3 u}{2 M} . . . . . . . . . . . . (2) F r o m e q u a t i o n s (1) a n d (2) w e g e t M = 1.2 k g$

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