Question

Two balls approach each other with same speed and undergo head on elastic collision, after which one of them (of mass 2 kg) comes to rest. The mass of other ball is
​

Answer 1

Answer:

the mass of ball is 4 kg as 2 balls and two balls with 2 kg

2x2=4

Explanation:

Answer 2

Two balls approach each other with same speed and undergo head on elastic collision, after which one of them (of mass 2 kg) comes to rest. The mass of other ball is 1.6kg.

Given:

$m_{1}$ = 2kg.

$u_{1} = - u_{2}$ (As speeds are same but in opposite direction)

To find:

$m_{2} = ?$

Solution:

Elastic Collision:

• The collision in which both kinetic energy and momentum remains conserved is elastic collision.

Coefficient of restitution:

• It is the ratio of initial relative speed to final relative speed among the colliding objects.
• Coefficient of restitution is 1 for perfectly elastic collisions.

Since, the collision is elastic coefficient of restitution is 1. Therefore, velocity of approach will be equal to velocity of separation.

$(v_{1}-v_{2} )=(u_{2}-u_{1} )\\\\0 - v_{2} = -u-u\\\\ v_{2} = 2u$

Using law of energy conservation:

$m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2} \\\\2u + m(-u) = 2(0) + m(2u)\\\\2u = 3mu\\\\m = \frac{2}{3} \\\\m = 1.6kg$

Therefore, two balls approach each other with same speed and undergo head on elastic collision, after which one of them (of mass 2 kg) comes to rest. The mass of other ball is 1.6kg.