Question

A body of mass 4 kg moving with a velocity of 9 m/s. Collides with a body of 8 kg at rest. The coefficient of restitution is 0.33. After collision the velocity of body having mass 4 kg is:

• A. 1 m/s
• B. 4 m/s
• C. 3 m/s
• D. 9 m/s

Answer 1

The correct option is C 3 m/s

Given,

$m_1=4kg$

$m_2=8kg$

$u_1=9m/s$

$u_2=0$ because body is at rest.

The coefficient of restitution , $e=0.33$

The coefficient of restitution $0<e<1$ the collision is inelastic, linear momentum is conserved. Final velocity are same $v$

By the conservation of linear momentum.

$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$

$m_1{u}_1=(m_1+m_2)v$

$v=\frac{m_1{u}_1}{m_1+m_2}$

$v=\frac{4\times 9}{4+8}$

$v=3m/s$