If a bullet of mass 5gm moving with velocity `100m//sec`, penertates the wooden block upto 6cm. Then the average force imposed by the bullet on the block is

Options

A. 8300N
B. 417N
C. 830N
D. zero

Explanation

To solve the problem, we need to calculate the average force exerted by the bullet on the wooden block when the bullet penetrates the block. We will use the concepts of kinematics and Newton's second law of motion.

### Step-by-Step Solution:

1. **Identify the given data:**
- Mass of the bullet, \( m = 5 \, \text{g} = 5 \times 10^{-3} \, \text{kg} \)
- Initial velocity of the bullet, \( u = 100 \, \text{m/s} \)
- Final velocity of the bullet after penetration, \( v = 0 \, \text{m/s} \) (since it comes to rest)
- Penetration depth, \( s = 6 \, \text{cm} = 6 \times 10^{-2} \, \text{m} \)

2. **Use the kinematic equation to find the retardation (deceleration):**
\[ v^2 = u^2 + 2as \]
Rearranging gives:
\[ a = \frac{v^2 - u^2}{2s} \]
Substituting the values:
\[ a = \frac{0^2 - (100)^2}{2 \times 6 \times 10^{-2}} = \frac{-10000}{0.12} = -83333.33 \, \text{m/s}^2 \]
(The negative sign indicates deceleration.)

3. **Calculate the average force using Newton's second law:**
\[ F = ma \]
Substituting the values:
\[ F = 5 \times 10^{-3} \, \text{kg} \times (-83333.33 \, \text{m/s}^2) = -416.67 \, \text{N} \]
(The negative sign indicates the direction of the force is opposite to the motion of the bullet.)

4. **Calculate the average force in magnitude:**
The average force exerted by the bullet on the block is approximately:
\[ F \approx 416.67 \, \text{N} \]

5. **Round the answer:**
The closest option is \( 417 \, \text{N} \).

### Final Answer:
The average force imposed by the bullet on the block is approximately **417 N**.

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