When a bullet of mass 10 g and speed 100 m/s penetrates up to distance 1 cm in a human body at rest. The resistance offered by human body is :

Options

A. 2000 N
B. 1500 N
C. 5000 N
D. 1000 N

Answer

To solve the problem, we need to determine the resistance offered by the human body when a bullet penetrates it. We will use the equations of motion to find the acceleration (or retardation) of the bullet and then calculate the force (resistance) using Newton's second law.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the bullet, \( m = 10 \, \text{g} = 0.01 \, \text{kg} \) (since 1 g = 0.001 kg)
- Initial speed of the bullet, \( u = 100 \, \text{m/s} \)
- Final speed of the bullet, \( v = 0 \, \text{m/s} \) (when it comes to rest)
- Distance penetrated, \( s = 1 \, \text{cm} = 0.01 \, \text{m} \)

2. **Use the Equation of Motion:**
We can use the equation of motion:
\[ v^2 = u^2 + 2as \]
Here, \( v = 0 \), \( u = 100 \, \text{m/s} \), and \( s = 0.01 \, \text{m} \). We need to find the acceleration \( a \).

Substituting the values:
\[ 0 = (100)^2 + 2a(0.01) \]
\[ 0 = 10000 + 0.02a \]
Rearranging gives:
\[ 0.02a = -10000 \]
\[ a = \frac{-10000}{0.02} = -500000 \, \text{m/s}^2 \]
(The negative sign indicates that this is a retardation.)

3. **Calculate the Force (Resistance):**
According to Newton's second law:
\[ F = ma \]
Where \( m = 0.01 \, \text{kg} \) and \( a = -500000 \, \text{m/s}^2 \):
\[ F = 0.01 \times (-500000) = -5000 \, \text{N} \]
The negative sign indicates that the force is acting in the opposite direction to the bullet's motion, which is expected for a resistance force.

4. **Final Result:**
The magnitude of the resistance offered by the human body is:
\[ F = 5000 \, \text{N} \]

### Summary:
The resistance offered by the human body when the bullet penetrates is **5000 N**.