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 wall in $0.1$ second, then the force will be:

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

Answer 1

Answer: (D)

$10\sqrt{3}N$

Change in momentum of the ball perpendicular to the wall

$=\text{m}[\text{v}cos\theta -(-\text{v}cos\theta \left)\right]$

$=2\text{mv}cos\theta$

$=2\times 1\times 1\times cos{30}^{\circ }=2\times \frac{\sqrt{3}}{2}=\sqrt{3}$,

Rate of change of momentum

$=\frac{\text{Change of momentum}}{\text{time}}=\frac{\sqrt{3}}{0.1}=10\sqrt{3}$

This will be equal to force, so force $=10\sqrt{3}N$