A bullet of mass 10g leaves a rifle at an intial velocity of 1000m/s and strikes the earth at the same level with a velocity of 500m/s. The work done in joule to overcome the resistance of air will be

Options

A. 375
B. 3750
C. 5000
D. 500

Answer

To solve the problem, we need to calculate the work done to overcome the resistance of air when a bullet is fired from a rifle. This can be determined by finding the change in kinetic energy of the bullet as it travels through the air.

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass of the bullet, \( m = 10 \, \text{g} = 0.01 \, \text{kg} \) (since 1 g = 0.001 kg)
- Initial velocity of the bullet, \( u = 1000 \, \text{m/s} \)
- Final velocity of the bullet, \( v = 500 \, \text{m/s} \)

2. **Calculate the initial kinetic energy (KE_initial):**
\[ KE_{\text{initial}} = \frac{1}{2} m u^2 \]
Substituting the values:
\[ KE_{\text{initial}} = \frac{1}{2} \times 0.01 \, \text{kg} \times (1000 \, \text{m/s})^2 \]
\[ KE_{\text{initial}} = \frac{1}{2} \times 0.01 \times 1000000 = 5000 \, \text{J} \]

3. **Calculate the final kinetic energy (KE_final):**
\[ KE_{\text{final}} = \frac{1}{2} m v^2 \]
Substituting the values:
\[ KE_{\text{final}} = \frac{1}{2} \times 0.01 \, \text{kg} \times (500 \, \text{m/s})^2 \]
\[ KE_{\text{final}} = \frac{1}{2} \times 0.01 \times 250000 = 1250 \, \text{J} \]

4. **Calculate the change in kinetic energy (ΔKE):**
\[ \Delta KE = KE_{\text{final}} - KE_{\text{initial}} \]
\[ \Delta KE = 1250 \, \text{J} - 5000 \, \text{J} = -3750 \, \text{J} \]

5. **Interpret the result:**
The negative sign indicates that the bullet lost energy due to air resistance. The work done to overcome the resistance of air is equal to the magnitude of the change in kinetic energy:
\[ \text{Work done} = 3750 \, \text{J} \]

### Final Answer:
The work done to overcome the resistance of air is **3750 Joules**.