Question

Two balls of masses $2\text{kg}$ and $4\text{kg}$ after the collision are moving with speeds $4\text{m/s}$ and $2\text{m/s}$ as shown in figure. Find the impulse of reformation for the $4\text{kg}$ ball.

• A. $4\text{N-s}$
• B. $2\text{N-s}$
• C. $8\text{N-s}$
• D. $1\text{N-s}$

Answer 1

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


Let $v$ be the common velocity at the time of maximum deformation.
Applying linear momentum conservation principle (taking rightward +ve):
$(m_1+m_2)v=m_1{v}_1+m_2{v}_2$
$(2+4)v=2\times (-4)+4\times \left(2\right)=0$
$\Rightarrow v=0$
Impulse of reformation:
$J_R=$ change in momentum of any body during reformation
$\therefore J_R=m_2(v_2-v)=4(2-0)=8\text{N-s}$