A cork is submerged in water by a spring attached to the bottom of a bowl. When the bowl is kept in an elevator moving with acceleration downwards, the length of spring.

Options

A. increases
B. decreases
C. remain unchanged
D. none of these

Explanation

To solve the problem of how the length of the spring changes when the bowl with the submerged cork is in an elevator moving downwards, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have a cork submerged in water, held down by a spring attached to the bottom of a bowl.
- The bowl is placed in an elevator that is accelerating downwards.

2. **Identify Forces Acting on the Cork**:
- The forces acting on the cork include:
- The buoyant force (thrust) acting upwards.
- The weight of the cork acting downwards.

3. **Consider the Effect of Downward Acceleration**:
- When the elevator accelerates downwards, the effective gravitational acceleration acting on the cork changes.
- The effective acceleration can be expressed as \( g' = g - a \), where \( g \) is the acceleration due to gravity and \( a \) is the downward acceleration of the elevator.

4. **Calculate the Buoyant Force**:
- The buoyant force (thrust) acting on the cork can be given by the formula:
\[ F_b = \rho V g' \]
- Substituting for \( g' \):
\[ F_b = \rho V (g - a) \]
- Here, \( \rho \) is the density of the fluid (water), \( V \) is the volume of the cork, and \( g' \) is the effective gravitational acceleration.

5. **Analyze the Change in Buoyant Force**:
- As the elevator accelerates downwards, \( g' \) decreases, which means the buoyant force \( F_b \) also decreases.
- This decrease in buoyant force results in less upward force acting on the cork.

6. **Effect on the Spring**:
- Since the buoyant force acting on the cork is reduced, the spring will not need to exert as much force to keep the cork submerged.
- As a result, the length of the spring will increase (it will stretch more) to accommodate the reduced buoyant force.

7. **Conclusion**:
- Therefore, when the elevator is moving downwards, the length of the spring will **increase**.

### Final Answer:
The length of the spring will **increase** when the bowl is kept in an elevator moving downwards.