The terminal velocity of a ball in air is v, where acceleration due to gravity is g. Now the same ball is taken in a gravity free space where all other conditions are same. The ball is now pushed at a speed v, then –

Options

A. the terminal velocity of the ball will be `(v)/(2)`
B. the ball with move with a contant velocity
C. the initial acceleration of the ball is `2g` in opposite direction of the ball's velocity
D. the ball with finally stop

Answer

To solve the problem step by step, we need to analyze the situation where a ball is in air and then taken to a gravity-free space.

### Step 1: Understanding Terminal Velocity in Air
In air, the terminal velocity \( v \) of the ball is achieved when the gravitational force acting on the ball is balanced by the drag force due to air resistance. The forces acting on the ball can be described as:
- Gravitational force: \( F_g = mg \)
- Drag force: \( F_d = \frac{1}{2} C_d \rho A v^2 \)

At terminal velocity, these forces are equal:
\[ mg = \frac{1}{2} C_d \rho A v^2 \]

Where:
- \( m \) is the mass of the ball,
- \( g \) is the acceleration due to gravity,
- \( C_d \) is the drag coefficient,
- \( \rho \) is the density of air,
- \( A \) is the cross-sectional area of the ball.

### Step 2: Transition to Gravity-Free Space
When the ball is taken to a gravity-free space, the gravitational force \( mg \) becomes zero. Therefore, there is no longer a force pulling the ball downwards.

### Step 3: Pushing the Ball at Speed \( v \)
In gravity-free space, if the ball is pushed at speed \( v \), it will continue to move at that speed indefinitely, as there is no opposing force (like gravity or drag) to slow it down.

### Step 4: Conclusion
Since there is no gravitational force acting on the ball in gravity-free space, and it is pushed at speed \( v \), the ball will not stop. It will continue to move at that speed indefinitely until acted upon by another force.

### Final Answer
The ball will continue to move at speed \( v \) indefinitely in gravity-free space.

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