Question

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

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

Answer 1

Answer: (D)

The impulse of the force between the two ball is (40 m) Ns.

Using Momentum Conservation:
$\Rightarrow m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2\Rightarrow m\left(21\right)+2m(-4)=m\left(1\right)+2m{v}_2\Rightarrow v_2=6m/s$
Coefficient of Restitution:

$e=\frac{v_2-v_1}{u_1-u_2}=\frac{6-1}{21+4}=0.2$
Kinetic Energy lost:

$=\frac{1}{2}{m}_1(v_1^2-u_1^2)+\frac{1}{2}{m}_2(v_2^2-u_2^2)$
$=\frac{1}{2}m(1-441)+\frac{1}{2}2m(36-16)=-200mJ$
Impulse of Force:
$I=(\Delta mv{)}_1=m(1-21)=-20m=(\Delta mv{)}_2=2m(6-(-4\left)\right)=20m$