Question

Two balls of masses $2\text{kg}$ and $4\text{kg}$ are moved towards each other with velocities $4\text{m/s}$ and $2\text{m/s}$ respectively on a frictionless surface. Find the impulse of maximum deformation for the ball of $4\text{kg}$ mass.

• A. $\frac{8}{3}\text{N-s}$
• B. $\frac{4}{3}\text{N-s}$
• C. $\frac{2}{3}\text{N-s}$
• D. $8\text{N-s}$

Answer 1

The correct option is D $8\text{N-s}$


Linear momentum is conserved for the system
Let $v$ be the common velocity during maximum deformation.
Applying linear momentum conservation equation :
$m_1{u}_1+m_2{u}_2=(m_1+m_2)v$
$v=\frac{(m_1{u}_1+m_2{u}_2)}{(m_1+m_2)}=\frac{2\times 4+4\times (-2)}{2+4}$
$v=0\text{m/s}$

Impulse of deformation
$J_D=$ change in momentum of any one body during deformation
For $4\text{kg},J_D=m_2(v-u_2)$
$=4(0-(-2\left)\right)=8\text{N-s}$