Question

a body of mass M moving with constant velocity collides head on with another stationary body of same mass if the coefficient of restitution between the bodies is 1 by 2 then ratio of velocities of two bodies after collision will be​

Answer 1

Ratio of velocities of two bodies after collision = $\bf{\frac{v_1}{v_2} = \frac{1}{3}}$

Explanation:

Suppose $v_1$ and $v_2$ are final velocities after collision.

According to the law of conservation of momentum,

$mv_1 + mv_2 = mv$

$v = v_1 + v_2$  .........(1)

coefficient of restitution,$e = \frac {velocity of separation} {velocity of approach}$

velocity of separation = $v_2-v_1$

Given

$\frac{1}{2} = \frac{v_2-v_1}{v}$

$\frac{1}{2}v = v_2-v_1$........(2)

Add (1) and (2)

$2v_2 = v + \frac{1}{2} v$

$v_2=\frac{3}{4}v$

$v_1= v-v_2$

$=\frac{1}{4}v$

$\frac{v_1}{v_2} = \frac{1}{3}$

Ratio of velocities of two bodies after collision = $\bf{\frac{v_1}{v_2} = \frac{1}{3}}$

Answer 2

Answer:

Here you go :)

Explanation:

Hope you liked it.