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Chapter 5: Problem 589

A player caught a cricket ball of mass \(150 \mathrm{gm}\) moving at a rate of \(20 \mathrm{~m} / \mathrm{s}\) If the catching process is Completed in \(0.1\) sec the force of the flow exerted by the ball on the hand of the player ..... N \(\\{\mathrm{A}\\} 3\) \(\\{B\\} 30\) \(\\{\mathrm{C}\\} 150\) \(\\{\mathrm{D}\\} 300\)

Short Answer

Expert verified
The force exerted by the ball on the hand of the player during the catching process is \(30 \mathrm{N}\). Therefore, the correct answer is B.

Step by step solution

01

Convert the mass to kilograms

The mass of the ball is given in grams. We need to first convert it to kilograms: \(150 \mathrm{gm} = 150 \times 10^{-3} \mathrm{kg}\).
02

Calculate the initial momentum of the ball

The initial momentum of the ball can be calculated using the formula: Momentum = mass × initial velocity Initial momentum = \( 150 \times 10^{-3} \mathrm{kg} \times 20 \mathrm{~m} / \mathrm{s} = 3 \mathrm{kg ~m} / \mathrm{s}\).
03

Calculate the final momentum of the ball

Since the player catches the ball and stops it, the final velocity of the ball is 0. Therefore, the final momentum of the ball will be: Final momentum = mass × final velocity Final momentum = \( 150 \times 10^{-3} \mathrm{kg} \times 0 \mathrm{~m} / \mathrm{s} = 0 \mathrm{kg ~m} / \mathrm{s}\).
04

Calculate the change in momentum

To calculate the change in momentum, we'll subtract the final momentum from the initial momentum: Change in momentum = Initial momentum - Final momentum Change in momentum = \(3 \mathrm{kg ~m} / \mathrm{s} - 0 \mathrm{kg ~m} / \mathrm{s} = 3 \mathrm{kg ~m} / \mathrm{s}\).
05

Calculate the force exerted by the ball on the hand of the player

The force required to change the momentum of the ball can be calculated using the formula: Force = change in momentum / Time taken for the change in momentum Force = \( \frac{(3 \mathrm{kg ~m} / \mathrm{s})}{0.1 \mathrm{s}} = 30 \mathrm{N} \). The force exerted by the ball on the hand of the player during the catching process is \(30 \mathrm{N}\). Therefore, the correct answer is B.

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Most popular questions from this chapter

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