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 find the resistance offered by the human body when a bullet penetrates it. We will use the concepts of kinematics and Newton's second law of motion.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the bullet (m) = 10 g = 10/1000 kg = 0.01 kg
- Initial speed of the bullet (u) = 100 m/s
- Final speed of the bullet (v) = 0 m/s (since it comes to rest)
- Distance penetrated (s) = 1 cm = 1/100 m = 0.01 m

2. **Use the Kinematic Equation:**
We will use the equation:
\[ v^2 = u^2 + 2as \]
Here, \(a\) is the acceleration (or retardation in this case since the bullet is slowing down).

3. **Substituting the Known Values:**
Plugging in the values we have:
\[ 0^2 = (100)^2 + 2a(0.01) \]
This simplifies to:
\[ 0 = 10000 + 0.02a \]

4. **Solving for Acceleration (a):**
Rearranging the equation to solve for \(a\):
\[ 0.02a = -10000 \]
\[ a = \frac{-10000}{0.02} = -500000 \, \text{m/s}^2 \]
(The negative sign indicates that this is a retardation.)

5. **Calculating the Force (Resistance):**
Using Newton's second law, \(F = ma\):
\[ F = m \cdot a = 0.01 \, \text{kg} \cdot (-500000 \, \text{m/s}^2) \]
\[ F = -5000 \, \text{N} \]
The negative sign indicates that the force is acting in the opposite direction to the motion of the bullet.

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

### Answer:
The resistance offered by the human body is **5000 Newton**.