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. The impulse of maximum deformation for the ball of $4\text{kg}$ mass is (in $N-s$)

• A. 8.00
• B. 8.0
• C. 8

Answer 1

Answer: (A), (B), (C)

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 $4\text{kg},J_D=m_2(v-u_2)$
$=4(0-(-2\left)\right)=8\text{N-s}$