A boby is moving in a room with a velocity of `20m//s` perpendicular to the two walls separated by 5 meters .There is no friction and the collisionnn with the walls are elastic.

Options

A. Not periodic
B. Periodic but not smple harmonic
C. Periodic and simple harmonic
D. Periodic with variable time period

Answer

To solve the problem, we need to analyze the motion of the body as it collides with the walls in the room. Here’s a step-by-step solution:

### Step 1: Understand the Setup
- The body is moving with a velocity of \(20 \, \text{m/s}\) perpendicular to two walls that are \(5 \, \text{m}\) apart.
- The collisions with the walls are elastic, meaning the body will bounce back with the same speed after hitting the walls.

### Step 2: Calculate the Time Taken for One Round Trip
- The body travels \(5 \, \text{m}\) to the first wall and then \(5 \, \text{m}\) back to the starting point after colliding with the second wall.
- The total distance for one complete round trip is:
\[ \text{Total Distance} = 5 \, \text{m} + 5 \, \text{m} = 10 \, \text{m} \]
- The time taken to travel this distance at a speed of \(20 \, \text{m/s}\) can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Velocity}} = \frac{10 \, \text{m}}{20 \, \text{m/s}} = 0.5 \, \text{s} \]

### Step 3: Determine the Nature of Motion
- Since the body returns to its starting position after \(0.5 \, \text{s}\), this indicates that the motion is periodic.
- However, for the motion to be classified as Simple Harmonic Motion (SHM), it must satisfy the condition that the acceleration is directly proportional to the displacement from the mean position and directed towards it.

### Step 4: Analyze if the Motion is SHM
- In this case, while the motion is periodic (the body keeps bouncing between the walls), it does not have a restoring force that is proportional to the displacement from a mean position (as required for SHM).
- Therefore, the motion is periodic but not SHM.

### Conclusion
- The correct classification of the motion is that it is periodic but not simple harmonic motion (SHM).

### Final Answer
The motion of the body is periodic but not SHM.

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