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. (a) zero
B. (b) `(2Mv)/(pi)`
C. (c) `MvR`
D. (d) `Mv`

Explanation

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

### Step 1: Understand the Problem
The train has a mass \( M \) and is moving with a constant speed \( v \) on a circular track of radius \( R \). The length of the train is half of the perimeter of the track.

### Step 2: Calculate the Perimeter of the Circular 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 have:
\[ \text{Length of the train} = \frac{1}{2} P = \frac{1}{2} \times 2\pi R = \pi R \]

### Step 3: Determine the Linear Momentum
Linear momentum \( p \) is given by the formula:
\[ p = M \cdot v \]
where \( M \) is the mass of the train and \( v \) is its velocity.

### Step 4: Substitute the Values
Since the train is moving with a constant speed \( v \), we can directly substitute the values into the momentum formula:
\[ p = M \cdot v \]

### Step 5: Conclusion
The linear momentum of the train is:
\[ p = Mv \]