Question

Two balls $A$ and $B$ having masses $1kg$ and $2kg$, moving with speeds $21m/s$ and $4m/s$ respectively in opposite direction, collide head on. After collision $A$ moves with a speed of $1m/s$ in the same direction, the correct statements is :

• A. The velocity of $B$ after collision is $6m/s$ opposite to the direction of motion before collision
• B. The coefficient of restitution is $0.2$
• C. The loss of kinetic energy due to collision is $200J$
• D. The impulse of the force between the two balls is $40Ns$

Answer 1

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

The velocity of $B$ after collision is $6m/s$ opposite to the direction of motion before collision
The coefficient of restitution is $0.2$
The loss of kinetic energy due to collision is $200J$

Using Momentum Conservation:
$\Rightarrow m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2\Rightarrow 1\left(21\right)+2(-4)=1\left(1\right)+2v_2\Rightarrow v_2=6m/s$
Coefficient of Restitution:
$e=\frac{v_2-v_1}{u_1-u_2}=\frac{6-1}{21+4}=0.2$
Kinetic Energy lost:
$=\frac{1}{2}{m}_1(v_1^2-u_1^2)+\frac{1}{2}{m}_2(v_2^2-u_2^2)=\frac{1}{2}1(1-441)+\frac{1}{2}2(36-16)=-200J$
Impulse of Force:
$I=(\Delta mv{)}_1=1(1-21)=-20=(\Delta mv{)}_2=2(6-(-4\left)\right)=20$