Question

A body of mass m1 collides elastically with another body of mass m2 at rest after collision the velocity of m1 becomes 3/4 times the initial velocity .Find the ratio of their masses??????????????

Answer 1

Answer:

The ratio of their masses is 1:7.

Explanation:

Given that,

Final velocity $v_{1}= \dfrac{3}{4}u_{1}$

Using conservation of momentum

Velocity of the first body after the collision when  second body is rest

$v_{1}=\dfrac{m_{1}-m_{2}}{m_{1}+m_{2}}u_{1}$

$\dfrac{3}{4}=\dfrac{m_{1}-m_{2}}{m_{1}+m_{2}}u_{1}$

$3(m_{1}+m_{2})=4(m_{1}-m_{2})$

$3m_{1}+3m_{2}=4m_{1}-4m_{2}$

$3m_{1}-4m_{1}=-4m_{2}-3m_{2}$

$-m_{1}=-7m_{2}$

The ratio of their masses is

$\dfrac{m_{1}}{m_{2}}=\dfrac{1}{7}$

Hence, The ratio of their masses is 1:7.