A metal ball falls through water with terminal velocity 20 `ms^(-1)`. When the ball is allowed to fall through vacuum, then

Options

A. Terminal velocity is 30 `ms^(-1)`
B. Terminal velocity is 20 `ms^(-1)`
C. Terminal velocity is 15 `ms^(-1)`
D. There is no terminal velocity

Answer

To solve the problem, we will analyze the forces acting on the metal ball in both scenarios: falling through water and falling through a vacuum.

### Step-by-Step Solution:

1. **Understanding Terminal Velocity in Water:**
- When the metal ball falls through water, it eventually reaches a point where the forces acting on it are balanced. The downward gravitational force (weight) of the ball, denoted as \( mg \), is balanced by the upward buoyant force \( B \) exerted by the water.
- At terminal velocity, the net force acting on the ball is zero, which means:
\[ mg = B \]
- The terminal velocity of the ball in water is given as \( 20 \, \text{m/s} \).

2. **Forces Acting on the Ball in Vacuum:**
- When the ball is allowed to fall through a vacuum, the only force acting on it is its weight \( mg \).
- In a vacuum, there is no fluid (like air or water) to provide buoyancy or drag forces. Thus, there are no opposing forces acting on the ball.

3. **Conclusion on Terminal Velocity in Vacuum:**
- Since there are no opposing forces in a vacuum, the ball will continue to accelerate downwards under the influence of gravity. Therefore, it will not reach a terminal velocity as there is no force to balance the weight of the ball.
- The conclusion is that the ball will keep accelerating indefinitely until it hits the ground.

4. **Final Answer:**
- The correct option is that the metal ball cannot attain a terminal velocity when falling through a vacuum.