Question

A cricket player catches a ball of mass 120 g moving with 25 m/s speed. If the catching process is completed in 0.1 s then the magnitude of force exerted by the ball on the hand of player will be (in SI unit):

• A. 24
• B. 12
• C. 25
• D. 30

Answer 1

The Correct Option is D

To solve the problem of determining the force exerted by the ball on the player's hand, we can use the impulse-momentum theorem. The impulse experienced by an object is equal to the change in momentum of the object. The formula we use is:

\(F \cdot \Delta t = \Delta p\)

• Where \(F\) is the force,
• \(\Delta t\) is the time duration (0.1 s in this case), and
• \(\Delta p\) is the change in momentum.

The change in momentum \(\Delta p\) is given by:

\(\Delta p = m(v_f - v_i)\)

• Where \(m\) is the mass of the ball (120 g = 0.12 kg),
• \(v_f\) is the final velocity (0 m/s, as the ball comes to rest), and
• \(v_i\) is the initial velocity (25 m/s).

Substituting the values:

\(\Delta p = 0.12 \cdot (0 - 25) = -3 \, \text{kg} \cdot \text{m/s}\)

According to the impulse-momentum theorem:

\(F \cdot 0.1 = -3\)

Solve for \(F\):

\(F = \frac{-3}{0.1} = -30 \, \text{N}\)

The negative sign indicates the force is in the opposite direction of the initial motion, but since we are asked for the magnitude, it is 30 N. Therefore, the correct answer is:

30

Answer 2

Given: - Mass of the ball: \( m = 120 \, \text{g} = 0.12 \, \text{kg} \) - Initial speed of the ball: \( v = 25 \, \text{m/s} \) - Time taken to catch the ball: \( t = 0.1 \, \text{s} \) - Final speed of the ball: \( v_f = 0 \, \text{m/s} \) (since the ball is caught and comes to rest)

Step 1: Calculating the Change in Momentum

The change in momentum (\( \Delta p \)) of the ball is given by:

\[ \Delta p = m \cdot (v_f - v) \]

Substituting the given values:

\[ \Delta p = 0.12 \cdot (0 - 25) \, \text{kg} \cdot \text{m/s} \] \[ \Delta p = -3 \, \text{kg} \cdot \text{m/s} \]

The negative sign indicates a decrease in momentum.

Step 2: Calculating the Force Exerted

The force exerted by the ball on the hand of the player is given by Newton’s second law:

\[ F = \frac{\Delta p}{t} \]

Substituting the values:

\[ F = \frac{-3}{0.1} \, \text{N} \] \[ F = -30 \, \text{N} \]

The magnitude of the force is:

\[ |F| = 30 \, \text{N} \]

Conclusion:

The magnitude of the force exerted by the ball on the hand of the player is \( 30 \, \text{N} \).