Question

A mass 2m moving with some speed is directly
approaching another mass m moving with
double speed. After some time, they collide
with coefficient of restitution 0.5. Ratio of their
respective speeds after collision is
(A) 23 (B) 3/2 (C) 2 (D) 1/2​

Answer 1

Answer:

Ratio of the speed after collision is (D) 1/2

Explanation:

As we know that there is no external force on the system of two masses

so here we can use momentum conservation

so we will have

$2m(v) + m(-2v) = 2m(v_1) + m(v_2)$

$2v_1 + v_2 = 0$

also by coefficient of restitution we know

$e = \frac{v_{2f} - v_{1f}}{v_{1i} - v_{2i}}$

now we have

$0.5 = \frac{v_2 - v_1}{v + 2v}$

$1.5 v = v_2 - v_1$

by solving above equations we have

$v_2 = v$

$v_1 = -0.5 v$

now ratio of their speed after collision is

$v_1 : v_2 = 1 : 2$

#Learn

Topic : collision and momentum conservation

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