A body (solid sphere) of mass m makes an elastic collision with another idential body at rest. Just after collision the angle between the velocity vector of one body with the initial line of motion is `15^(@)` then the angle between velocity vector of the other body with the initial line of motion is

Options

A. `75^(@)`
B. `60^(@)`
C. `45^(@)`
D. `30^(@)`

Explanation

To solve the problem of the elastic collision between two identical bodies, we can follow these steps:

### Step 1: Understand the Problem
We have two identical solid spheres. One sphere is moving with an initial velocity \( v_0 \) and collides elastically with another identical sphere that is initially at rest. After the collision, the angle between the velocity vector of the first body (which was initially moving) and the initial line of motion is given as \( 15^\circ \).

### Step 2: Analyze the Collision
In an elastic collision between two identical bodies, the component of velocity along the line of impact gets exchanged. This means that:
- The body that was initially moving will have a new velocity vector after the collision.
- The body that was initially at rest will start moving with a velocity vector.

### Step 3: Identify Angles
Let’s denote:
- The angle made by the first body (initially moving) with the initial line of motion as \( \theta_1 = 15^\circ \).
- The angle made by the second body (initially at rest) with the initial line of motion as \( \theta_2 \).

Since the two bodies are identical and the collision is elastic, the angles they make with the initial line of motion will be complementary to each other due to the conservation of momentum and the nature of elastic collisions.

### Step 4: Use the Complementary Angle Property
In an elastic collision, if one body moves at an angle \( \theta_1 \) with respect to the initial line of motion, the other body will move at an angle \( \theta_2 \) such that:
\[ \theta_1 + \theta_2 = 90^\circ \]
Given that \( \theta_1 = 15^\circ \), we can find \( \theta_2 \):
\[ \theta_2 = 90^\circ - \theta_1 = 90^\circ - 15^\circ = 75^\circ \]

### Conclusion
Thus, the angle between the velocity vector of the second body (initially at rest) with the initial line of motion is \( 75^\circ \).

### Final Answer:
The angle between the velocity vector of the other body with the initial line of motion is \( 75^\circ \).

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