An object of mass m1 collides with another object of mass m2, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses m2: m1 is :

Question

An object of mass m1 collides with another object of mass m2, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses m2: m1 is : (A) 3: 1 (B) 2: 1 (C) 1: 2 (D) 1: 1

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/ef226fb2e1db3031523382c9853cfb93-.png" /> m 1 v 1=- m 1 v + m 2 v v 1=- v +( m 2/ m 1) v (( v 1+ v )/ v )=( m 2/ m 1) e =(2 v / v 1)=1 v =( v 1/2) ( v 1+ v 1 / 2/ v 1 / 2)=( m 2/ m 1) 3=( m 2/ m 1)

Q. An object of mass $m_{1}$ collides with another object of mass $m_{2}$ , which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses $m_{2} : m_{1}$ is :

3 : 1

2 : 1

1 : 2

1 : 1

$m_{1} v_{1} = - m_{1} v + m_{2} v$
$v_{1} = - v + \frac{m _{2}}{m _{1}} v$
$\frac{( v _{1} + v )}{v} = \frac{m _{2}}{m _{1}}$
$e = \frac{2 v}{v _{1}} = 1$
$v = \frac{v _{1}}{2}$
$\frac{v _{1} + v _{1} /2}{v _{1} /2} = \frac{m _{2}}{m _{1}}$
$3 = \frac{m _{2}}{m _{1}}$

Q. An object of mass m1​ collides with another object of mass m2​, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses m2​:m1​ is :