Question

A cricketer catches a ball of mass 150 gm in 0.1 sec moving with speed 20 m/s, then he experiences force of

• A. 300 N
• B. 30 N
• C. 3 N
• D. 0.3 N

Answer 1

The Correct Option is B

To calculate the force experienced by the cricketer while catching the ball, we can use the concept of impulse and the formula for force.

Impulse is defined as the change in momentum of an object when a force is applied over time. The formula is given by:

F \cdot \Delta t = \Delta p

Where:

• F is the force applied (in Newtons)
• \Delta t is the time over which the force is applied (in seconds)
• \Delta p is the change in momentum (in kg·m/s)

The change in momentum \Delta p can be calculated as:

\Delta p = m \cdot \Delta v

Where:

• m is the mass of the object (in kg)
• \Delta v is the change in velocity (in m/s)

Given that the mass of the ball is 150 g, we first convert it to kg:

m = \frac{150}{1000} = 0.15 \, \text{kg}

The initial velocity v_i is 20 m/s, and the final velocity v_f is 0 m/s (as the ball is caught and comes to rest). Thus, the change in velocity is:

\Delta v = v_f - v_i = 0 - 20 = -20 \, \text{m/s}

Now, substituting the values into the change in momentum formula:

\Delta p = 0.15 \cdot (-20) = -3 \, \text{kg}\cdot\text{m/s}

The negative sign indicates a decrease in momentum as the ball slows down.

The time duration \Delta t over which the force is applied is given as 0.1 seconds.

Substituting the values of \Delta p and \Delta t into the impulse formula:

F = \frac{\Delta p}{\Delta t} = \frac{-3}{0.1} = -30 \, \text{N}

The negative sign indicates that the force is in the opposite direction to the motion of the ball. Thus, the magnitude of the force experienced is:

30 \, \text{N}

Therefore, the cricketer experiences a force of 30 N. The correct option is 30 N.