A ball having velocity v towards the right and having angular velocity clockwise approaches the wall. It collides elastically with wall and moves towards the left . Ground and wall are frictionless. Select the correct statement about the angular velocity of the ball after the collision .

Options

A. It will be anti - clockwise
B. It becomes zero
C. Angular speed decreases
D. It will be clockwise

Answer

To solve the problem, we need to analyze the situation step by step:

### Step 1: Understand the Initial Conditions
The ball is moving towards the right with a velocity \( v \) and has an angular velocity that is clockwise.

**Hint:** Identify the direction of both linear and angular velocities before the collision.

### Step 2: Analyze the Collision
The ball collides elastically with the wall. In an elastic collision, both momentum and kinetic energy are conserved. However, since the wall is frictionless, we need to focus on how the collision affects the ball's linear and angular velocities.

**Hint:** Recall the properties of elastic collisions and how they affect velocities.

### Step 3: Determine the Linear Velocity After Collision
After the collision, the ball moves towards the left with the same speed \( v \) (but in the opposite direction). This is due to the elastic nature of the collision.

**Hint:** Remember that the speed remains the same in an elastic collision, but the direction changes.

### Step 4: Analyze the Effect on Angular Velocity
Since the wall and ground are frictionless, there is no tangential force acting on the ball during the collision. The normal forces exerted by the wall act through the center of the ball, which means they do not create any torque about the center of the ball.

**Hint:** Consider how torque is related to angular acceleration and how forces act on the ball.

### Step 5: Conclusion on Angular Velocity
Because there is no torque acting on the ball (the tangential torque is zero), there is no angular acceleration. Therefore, the angular velocity of the ball remains unchanged in magnitude and direction. Since it was initially clockwise, it will still be clockwise after the collision.

**Hint:** Recall the relationship between torque, angular acceleration, and angular velocity.

### Final Answer
The angular velocity of the ball after the collision remains in the clockwise direction.

**Correct Statement:** The angular velocity of the ball after the collision remains clockwise.