A bullet hits a lock kept at rest on a smooth horizontal surface and gets embedded into it. Which of the following does not change?

Options

A. a linear momentum of the block
B. kinetic energy of the block
C. gravitational potential energy of the block
D. temperature of the block

Answer

To solve the problem, we need to analyze the situation of a bullet hitting a block on a smooth horizontal surface and determine which quantity does not change after the collision.

### Step-by-Step Solution:

1. **Identify the Initial Conditions**:
- A bullet is moving with an initial velocity \( u \) and strikes a block that is initially at rest on a smooth horizontal surface.

2. **Understand the Collision**:
- When the bullet embeds itself into the block, they move together after the collision. This is an inelastic collision.

3. **Analyze Linear Momentum**:
- Before the collision, the total linear momentum is given by the momentum of the bullet since the block is at rest:
\[ p_{\text{initial}} = m_{\text{bullet}} \cdot u + m_{\text{block}} \cdot 0 = m_{\text{bullet}} \cdot u \]
- After the collision, the bullet and block move together with a common velocity \( v \):
\[ p_{\text{final}} = (m_{\text{bullet}} + m_{\text{block}}) \cdot v \]
- Since momentum is conserved in a closed system, the linear momentum of the bullet and block will change due to the collision.

4. **Analyze Kinetic Energy**:
- The initial kinetic energy of the system is:
\[ KE_{\text{initial}} = \frac{1}{2} m_{\text{bullet}} u^2 + 0 \]
- After the collision, the kinetic energy of the combined system is:
\[ KE_{\text{final}} = \frac{1}{2} (m_{\text{bullet}} + m_{\text{block}}) v^2 \]
- Since some kinetic energy is transformed into other forms of energy (like heat due to deformation), the kinetic energy will change.

5. **Analyze Gravitational Potential Energy**:
- The block is on a horizontal surface, and there is no change in height during the collision. Therefore, the gravitational potential energy remains constant:
\[ PE = m \cdot g \cdot h \]
- Since \( h \) does not change, the gravitational potential energy does not change.

6. **Analyze Temperature**:
- When the bullet strikes the block, some kinetic energy is converted into heat due to friction and deformation, which will increase the temperature of the block. Therefore, the temperature will change.

### Conclusion:
The quantity that does not change after the bullet embeds into the block is the **gravitational potential energy of the block**.

### Final Answer:
**Gravitational potential energy of the block does not change.**

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