A player catches a ball of 200 gm moving with a speed of 20 m/s. if the time taken to complete the cathc is 0.5s, the force exerted on the player, hand is :-

Options

A. 8 N
B. 4N
C. 2N
D. 0N

Explanation

To solve the problem of finding the force exerted on the player's hand when catching a ball, we can follow these steps:

### Step 1: Understand the Given Data
- Mass of the ball (m) = 200 grams = 0.2 kg (since 1 kg = 1000 grams)
- Initial speed of the ball (u) = 20 m/s
- Final speed of the ball (v) = 0 m/s (the ball comes to rest when caught)
- Time taken to catch the ball (t) = 0.5 s

### Step 2: Calculate the Change in Momentum
The change in momentum (Δp) can be calculated using the formula:
\[ \Delta p = m(v - u) \]
Substituting the values:
\[ \Delta p = 0.2 \, \text{kg} \times (0 \, \text{m/s} - 20 \, \text{m/s}) = 0.2 \, \text{kg} \times (-20 \, \text{m/s}) = -4 \, \text{kg m/s} \]

### Step 3: Calculate the Force
Using Newton's second law, the force (F) can be calculated as:
\[ F = \frac{\Delta p}{t} \]
Substituting the values:
\[ F = \frac{-4 \, \text{kg m/s}}{0.5 \, \text{s}} = -8 \, \text{N} \]

### Step 4: Interpret the Result
The negative sign indicates that the force exerted by the player's hand is in the opposite direction to the initial velocity of the ball.

### Final Answer
The magnitude of the force exerted on the player's hand is **8 N** in the opposite direction of the ball's initial motion.

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