Question

A $1\text{kg}$ particle strikes a wall with a velocity $1\text{m/s}$ at an angle ${30}^{\circ }$ and reflects at the same angle in $0.1$ second, then the force applied by the wall on the particle will be

• A. $30\sqrt{3}\text{N}$
• B. $0$
• C. $40\sqrt{3}\text{N}$
• D. $10\sqrt{3}\text{N}$

Answer 1

The correct option is D $10\sqrt{3}\text{N}$

Velocity component only changes perpendicular to the wall and remains unchanged along the wall.

Therefore, change in momentum of the ball perpendicular to the wall
$△p=p_2-p_1=m[v\cos \theta -(-v\cos \theta \left)\right]$
$△p=2mv\cos \theta$
$△p=2\times 1\times 1\times \cos {30}^{\circ }=2\times \frac{\sqrt{3}}{2}=\sqrt{3}$,
Force = Rate of change of momentum
$F=\frac{\text{Change of momentum}}{\text{time}}$
$F=\frac{\sqrt{3}}{0.1}=10\sqrt{3}$
So force $=10\sqrt{3}\text{N}$.