Question

A body of mass \(5\) kg collides with a wall with a speed of \(50\,\text{m s}^{-1}\) and rebounds with the same speed. If the time of contact of the body with the wall is \(\frac{1}{20}\) s, the force exerted on the wall is

• A. \(0.5\times 10^{4}\,\text{N}\)
• B. \(2.5\times 10^{4}\,\text{N}\)
• C. \(2\times 10^{3}\,\text{N}\)
• D. \(1\times 10^{4}\,\text{N}\)
• E. \(4\times 10^{3}\,\text{N}\)

Hint:

When a body rebounds, always take velocity in opposite direction as negative. This doubles the change in momentum.

Answer 1

The Correct Option is D

Step 1: Write the given quantities.
Mass: \[ m=5\,\text{kg} \] Initial velocity: \[ u=50\,\text{m s}^{-1} \] Final velocity (rebounds in opposite direction): \[ v=-50\,\text{m s}^{-1} \] Time of contact: \[ t=\frac{1}{20}\,\text{s} \]

Step 2: Calculate change in velocity.
\[ \Delta v=v-u=-50-50=-100\,\text{m s}^{-1} \]

Step 3: Use the impulse-momentum theorem.
\[ \text{Force}=\frac{\text{Change in momentum}}{\text{time}} \] \[ F=\frac{m\Delta v}{t} \]

Step 4: Substitute values.
\[ F=\frac{5\times (-100)}{1/20} \]

Step 5: Simplify.
\[ F=\frac{-500}{1/20}=-500\times 20=-10000\,\text{N} \]

Step 6: Interpret the result.
The negative sign indicates direction. The magnitude of force exerted is: \[ |F|=10000\,\text{N} \]

Step 7: Final answer.
\[ \boxed{1\times 10^{4}\,\text{N}} \] which matches option \((4)\).