`A` lead bullet of `10g` travelling at `300m//s` strikes against a block of wood and comes to rest. Assuming `50%` heat is absorbed by the bullet, the increase in its temperature is (sp-heat of lead is `150J//Kg-K`)

Options

A. `100^(@)C`
B. `125^(@)C`
C. `150^(@)C`
D. `200^(@)C`

Explanation

To solve the problem step by step, we will calculate the increase in temperature of the lead bullet after it strikes the block of wood.

### Step 1: Calculate the Kinetic Energy of the Bullet
The kinetic energy (KE) of the bullet can be calculated using the formula:
\[ KE = \frac{1}{2} mv^2 \]
where:
- \( m \) is the mass of the bullet in kilograms,
- \( v \) is the velocity of the bullet in meters per second.

Given:
- Mass of the bullet, \( m = 10 \, \text{g} = 10/1000 \, \text{kg} = 0.01 \, \text{kg} \)
- Velocity, \( v = 300 \, \text{m/s} \)

Substituting the values:
\[ KE = \frac{1}{2} \times 0.01 \times (300)^2 \]
\[ KE = \frac{1}{2} \times 0.01 \times 90000 \]
\[ KE = 0.005 \times 90000 = 450 \, \text{J} \]

### Step 2: Calculate the Heat Absorbed by the Bullet
Since 50% of the kinetic energy is absorbed by the bullet, we calculate the heat absorbed by the bullet (\( Q \)):
\[ Q = \frac{1}{2} \times KE = \frac{1}{2} \times 450 = 225 \, \text{J} \]

### Step 3: Use the Heat Absorbed to Find the Increase in Temperature
The heat absorbed can also be expressed using the formula:
\[ Q = m \cdot C \cdot \Delta T \]
where:
- \( m \) is the mass of the bullet,
- \( C \) is the specific heat capacity of lead,
- \( \Delta T \) is the change in temperature.

Given:
- Specific heat capacity of lead, \( C = 150 \, \text{J/kg/K} \)

Substituting the known values:
\[ 225 = 0.01 \cdot 150 \cdot \Delta T \]

### Step 4: Solve for \( \Delta T \)
Rearranging the equation to solve for \( \Delta T \):
\[ \Delta T = \frac{225}{0.01 \cdot 150} \]
\[ \Delta T = \frac{225}{1.5} = 150 \, \text{K} \]

### Conclusion
The increase in temperature of the lead bullet is \( 150 \, \text{K} \) or \( 150 \, \text{°C} \).

### Final Answer
The increase in temperature is **150 °C**.

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