A cricket ball of mass 150 g is moving with a velocity of 12 m/s and is hit by a bat so that the ball is turned back with a velocity of 20 m/s. If duration of contact between the ball and the bat is 0.01 sec. The impulse of the force is :

Question

Accepted Answer

To determine the impulse of the force exerted on the cricket ball, we need to calculate the change in momentum of the ball. Impulse is defined as the change in momentum, and it can be calculated using the formula:

$$ \text{Impulse} = \Delta p = m \cdot \Delta v $$

where:
- $ m $ is the mass of the ball,
- $ \Delta v $ is the change in velocity.

Given:
- Mass of the ball, $ m = 150 \, \text{g} = 0.15 \, \text{kg} $ (since 1 g = 0.001 kg),
- Initial velocity of the ball, $ v_i = 12 \, \text{m/s} $,
- Final velocity of the ball, $ v_f = -20 \, \text{m/s} $ (negative because the direction is reversed).

The change in velocity, $ \Delta v $, is calculated as:

$$ \Delta v = v_f - v_i = -20 \, \text{m/s} - 12 \, \text{m/s} = -32 \, \text{m/s} $$

Now, calculate the impulse:

$$ \text{Impulse} = m \cdot \Delta v = 0.15 \, \text{kg} \cdot (-32 \, \text{m/s}) = -4.8 \, \text{N-s} $$

The magnitude of the impulse is $ 4.8 \, \text{N-s} $. Since impulse is a vector quantity and we are interested in the magnitude, the correct answer is 4.8 N-s, which corresponds to Option 1.

**Explanation for why other options are incorrect:**

- **Option 2 (7.4 N-S):** This value is incorrect because it does not match the calculated impulse of 4.8 N-s. The calculation of impulse based on the given mass and change in velocity does not result in 7.4 N-s.

- **Option 3 (1.2 N-S):** This value is incorrect as it significantly underestimates the impulse. The change in velocity and mass of the ball result in a much larger impulse than 1.2 N-s.

- **Option 4 (4.7 N-S):** This value is close but still incorrect. The precise calculation yields 4.8 N-s, not 4.7 N-s. Even a small deviation from the correct value is not acceptable in precise calculations.

Thus, the correct answer is Option 1, 4.8 N-S, based on the accurate calculation of the impulse using the given data.