A solid block is lying on a smooth horizontal table. A bullet hits and gets embedded in it. The physical quantity conserved is

Options

A. kinetic energy alone
B. momentum alone
C. both kinetic energy and momentum
D. power alone

Answer

To solve the problem, we need to analyze the situation where a bullet hits a solid block and gets embedded in it. We will determine which physical quantity is conserved during this collision.

### Step-by-Step Solution:

1. **Identify the System**:
We have a bullet and a solid block. The bullet is moving towards the block, and upon impact, it embeds itself into the block.

**Hint**: Consider the objects involved in the collision and their initial states.

2. **Understand the Collision**:
The bullet comes with an initial velocity and has kinetic energy. After the collision, the bullet and the block move together as one system.

**Hint**: Think about what happens to the velocities of the bullet and block after the collision.

3. **Conservation of Momentum**:
In a closed system where no external forces are acting, the total momentum before the collision is equal to the total momentum after the collision.

- Before the collision, the momentum of the bullet is \( p_{bullet} = m_{bullet} \cdot v_{bullet} \) and the block is at rest, so its momentum is \( p_{block} = 0 \).
- After the collision, the combined mass (bullet + block) moves with a common velocity \( v_{final} \).

The equation for conservation of momentum can be written as:
\[ m_{bullet} \cdot v_{bullet} + m_{block} \cdot 0 = (m_{bullet} + m_{block}) \cdot v_{final} \]

**Hint**: Remember that momentum is a vector quantity and consider the direction of the bullet's velocity.

4. **Kinetic Energy Consideration**:
Kinetic energy is given by the formula \( KE = \frac{1}{2}mv^2 \). Before the collision, only the bullet has kinetic energy. After the collision, the kinetic energy of the system changes because some kinetic energy is transformed into other forms of energy (like heat, sound, etc.) when the bullet embeds itself in the block.

- Initial kinetic energy of the bullet: \( KE_{initial} = \frac{1}{2} m_{bullet} v_{bullet}^2 \)
- Final kinetic energy of the combined system: \( KE_{final} = \frac{1}{2} (m_{bullet} + m_{block}) v_{final}^2 \)

Since \( KE_{final} < KE_{initial} \), kinetic energy is not conserved.

**Hint**: Compare the initial and final kinetic energies to see if they are equal.

5. **Conclusion**:
The only physical quantity that is conserved in this scenario is momentum. Therefore, the answer to the question is that momentum is conserved.

**Final Answer**: The physical quantity conserved is **momentum**.