If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest (in cm) ?

Question

Accepted Answer

To determine how much further the body will penetrate before coming to rest, we need to understand the relationship between the velocity of the body and the distance it penetrates into the wooden block.

### Explanation for Option 1:

1. **Initial Condition**: The body loses half of its velocity after penetrating 3 cm into the wooden block. This implies that the kinetic energy of the body is reduced to one-fourth of its initial value because kinetic energy is proportional to the square of the velocity ($KE \propto v^2$).

2. **Energy Consideration**: Initially, the body has full kinetic energy. After penetrating 3 cm, it has one-fourth of its initial kinetic energy remaining. This means that three-fourths of the initial kinetic energy has been used to penetrate the first 3 cm.

3. **Further Penetration**: The remaining one-fourth of the kinetic energy will be used to penetrate further into the block. Since three-fourths of the energy was used to penetrate 3 cm, the remaining one-fourth will allow the body to penetrate an additional 1 cm before coming to rest. This is because the penetration distance is directly proportional to the energy used.

Thus, the body will penetrate 1 cm more before coming to rest, making Option 1 the correct answer.

### Explanation for Why Other Options are Incorrect:

- **Option 2 (2 cm)**: This option suggests that the body would penetrate an additional 2 cm. However, since only one-fourth of the initial kinetic energy remains after the first 3 cm, it is not possible for the body to penetrate twice the distance (2 cm) with only one-fourth of the energy.

- **Option 3 (3 cm)**: This option implies that the body would penetrate an additional 3 cm, which would mean it penetrates the same distance with only one-fourth of the energy. This is not feasible because the energy required to penetrate is directly proportional to the distance.

- **Option 4 (1.5 cm)**: This option suggests that the body would penetrate an additional 1.5 cm. However, since the remaining kinetic energy is only one-fourth of the initial energy, it cannot penetrate 1.5 cm, which would require more energy than is available.

In conclusion, based on the energy considerations and the relationship between kinetic energy and penetration distance, Option 1 (1 cm) is the correct answer.