A player caught a cricket ball of mass 150 g moving at a rate of 20 m/s. If the catching process is

Q: Why do we need to convert the mass to kilograms?

In physics, the standard unit of force is the Newton (N), which is defined as $1\text{ kg}\cdot\text{m/s}^2$. If you leave the mass in grams, your resulting force will be off by a factor of 1000!

Q: What exactly is impulse?

Impulse is the product of the average force applied to an object and the time interval over which it acts. According to the Impulse-Momentum Theorem, this is exactly equal to the object's change in momentum.

Q: Why is the final momentum zero?

The problem states that the player 'caught' the ball. When you catch a ball, you bring it to a complete stop relative to your hand, meaning its final velocity—and therefore its final momentum—is zero.

Q: Does the ball exert the same force on the hand as the hand exerts on the ball?

Yes! According to Newton's Third Law of Motion, every action has an equal and opposite reaction. The hand pushes on the ball to stop it, and the ball pushes back on the hand with the exact same amount of force.

Q: Why do cricketers pull their hands back when catching a fast ball?

By pulling their hands back, they increase the time interval ($\Delta t$) over which the ball comes to a stop. Since the change in momentum ($\Delta p$) is constant, a larger $\Delta t$ results in a smaller force ($F$), preventing injury to their hands.

Question

A player caught a cricket ball of mass $150	ext{ g}$ moving at a rate of $20	ext{ m/s}$. If the catching process is completed in $0.1	ext{ s}$, the force of the blow exerted by the ball on the hand of the player is equal to

Options:

(A) $150	ext{ N}$

(B) $3	ext{ N}$

(C) $30	ext{ N}$

(D) $300	ext{ N}$

Sigma Percentile · Accepted Answer

### The Physics of a Cricket Catch

Imagine you are standing on the field, and a cricket ball is flying towards your hands. The ball has a mass of $150	ext{ g}$ and is moving at a blistering speed of $20	ext{ m/s}$. When you catch it, you bring it to a complete stop in just $0.1	ext{ s}$. Have you ever wondered exactly how much force that ball exerts on your hands? Let's dive into the physics behind this everyday sports phenomenon.

### The Master Equation: Impulse and Momentum

To solve this, we need to use a beautiful concept in physics known as the **Impulse-Momentum Theorem**. This theorem states that the impulse applied to an object is exactly equal to its change in momentum.

Mathematically, it is written as:

$$F \cdot \Delta t = \Delta p$$

Where $F$ is the average force, $\Delta t$ is the time interval, and $\Delta p$ is the change in momentum.

### Calculating the Change in Momentum

First, we must ensure all our units are in the standard SI format. The mass of the ball is $150	ext{ g}$, which we convert to kilograms:

$$m = 0.15	ext{ kg}$$

The initial momentum ($p_i$) of the ball is its mass times its initial velocity:

$$p_i = m \cdot v_i = 0.15 	imes 20 = 3	ext{ kg m/s}$$

Since you catch the ball and bring it to a complete stop, its final velocity is zero, making its final momentum ($p_f$) zero as well. Therefore, the magnitude of the change in momentum is simply $3	ext{ kg m/s}$.

### Finding the Force

Now, we substitute our known values into the Impulse-Momentum equation. We know the change in momentum is $3	ext{ kg m/s}$, and the time it took to stop the ball is $0.1	ext{ s}$.

$$F \cdot 0.1 = 3$$

To find the force, we simply divide the change in momentum by the time interval:

$$F = \frac{3}{0.1} = 30	ext{ N}$$

The ball exerts a force of **$30	ext{ N}$** on your hand!

### The Way Forward: Why Cricketers Pull Their Hands Back

This equation reveals a crucial secret about sports. Notice that the force $F$ and the time interval $\Delta t$ are inversely proportional for a given change in momentum.

If you were to catch the ball rigidly without pulling your hands back, the collision time might be as short as $0.01	ext{ s}$. In that case, the force would skyrocket to $300	ext{ N}$, which could easily injure your hand! By pulling their hands back, cricketers deliberately increase $\Delta t$, which drastically reduces the force $F$ they feel. Physics isn't just in textbooks; it's saving hands on the cricket pitch every day!

Animated Solution for Physics - Laws of Motion: A player caught a cricket ball of mass $150 g$ moving at a rate of $20 m/s$ . If the catching process is completed in $0.1 s$ , the force of the blow exerted by the ball on the hand of the player is equal to

Select Answer:

Visualized Solution

$Visualizing the Setup$

$The Impulse-Momentum Theorem$

$Calculating Initial Momentum$

$Change in Momentum$

$Applying the Equation$

$Final Calculation$

$The Physics of Catching$

The Sigma Insight: Inertia, Momentum, and Impulse

The Physics of a Cricket Catch

The Master Equation

Calculating the Change in Momentum

Finding the Force

The Way Forward

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