Question

Two billiard balls $A$ and $B,$ each of mass $50 \,g$ and moving in opposite directions with speed of $5\, m$ $s^{-1}$ each, collide and rebound with the same speed. The impulse imparted to each ball is

• A. $0.25\, kg \,m$ $s^{-1}$
• B. $0.5 \,kg\, m$ $s^{-1}$
• C. $0.1 kg \,m$ $s^{-1}$
• D. $0.125\, kg \,m$ $s^{-1}$

Answer 1

Answer: (B)

Initial momentum of ball $A$ $=\left(0.05 \, kg\right)$ $\left(5 \,m\,s^{-1}\right)$
$=0.25 \,kg \,m$ $s^{-1}$
As the speed is reversed on collision,
Final momentum of the ball $A$ $=\left(0.05 \,kg\right)$ $\left(-5 \,m \,s^{-1}\right)$
$=-0.25\, kg \,m$ $s^{-1}$
Impulse imparted to the ball $A$
= Change in momentum of ball $A$
= Final momentum - Initial momentum
$=-0.25 \,kg \, m$ $s^{-1}$ $-0.25 \,kg \,m$ $s^{-1}$ $=-0.5 \, kg \,m $$s^{-1}$
Similarly,
Initial momentum of ball $B$ $=\left(0.05\,kg\right)$ $\left(-5 \,m\, s^{-1}\right)$
$=-0.25\, kg$ $m\, s^{-1}$
Final momentum of ball B=$\left(0.05\,kg\right)\left(5 m \,s^{-1}\right)$
$=+0.25\, kg$ $m\, s^{-1}$
Impulse imparted to ball $B$ $=\left(0.25 \,kg \,m \,s^{-1}\right)$
$-\left(-0.25 \,kg \,m \,s^{-1}\right)$
$=0.5 \,kg\, m$ $s^{-1}$
Impulse imparted to each ball is $0.5\, kg\, m $ $s^{-1}$ in magnitude. The two impulses are opposite in direction.