A train of mass M is moving on a circular track of radius R with constant speed `v`. The length of the train is half of the perimeter of the track. The linear momentum of the train will be

Options

A. `piMv`
B. `(2Mv)/(pi)`
C. `(piMv)/2)`
D. Mv

Explanation

To solve the problem of finding the linear momentum of a train moving on a circular track, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
- We have a train of mass \( M \) moving on a circular track of radius \( R \) with constant speed \( v \).
- The length of the train is half of the perimeter of the track.

2. **Calculate the Perimeter of the Track**:
- The perimeter \( P \) of a circular track is given by the formula:
\[ P = 2\pi R \]
- Since the length of the train is half of the perimeter, we can express the length \( L \) of the train as:
\[ L = \frac{1}{2} P = \frac{1}{2} \times 2\pi R = \pi R \]

3. **Determine the Linear Momentum**:
- Linear momentum \( p \) is defined as the product of mass and velocity:
\[ p = M \cdot v \]
- Since the train is moving with a constant speed \( v \), the linear momentum of the train is simply:
\[ p = Mv \]

4. **Conclusion**:
- The linear momentum of the train moving on the circular track is:
\[ \boxed{Mv} \]