A chain of length 'L' and mass 'M' is hanging by fixing its upper end to a rigid support. The tension in the chain at a distance 'x' from the rigid support is

Options

A. Zero
B. Mg
C. `(Mg(L-x))/(L)`
D. `(Mg(L-x))/(x)`

Answer

To find the tension in a chain of length \( L \) and mass \( M \) hanging from a rigid support at a distance \( x \) from the support, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a chain of length \( L \) and mass \( M \) hanging vertically from a rigid support.
- We need to find the tension \( T \) at a point \( P \) which is at a distance \( x \) from the support.

2. **Identifying the Length Below Point P**:
- The length of the chain that is hanging below point \( P \) is \( L - x \). This is because the total length of the chain is \( L \) and the distance from the support to point \( P \) is \( x \).

3. **Calculating the Weight of the Chain Segment**:
- The weight of the segment of the chain that is hanging below point \( P \) can be calculated using the formula:
\[ \text{Weight} = \text{mass} \times \text{gravity} = (M/L) \times g \times (L - x) \]
- Here, \( M/L \) is the mass per unit length of the chain, and \( g \) is the acceleration due to gravity.

4. **Finding the Tension at Point P**:
- The tension \( T \) at point \( P \) is equal to the weight of the segment of the chain that is hanging below it. Therefore:
\[ T = \text{Weight of the segment below P} = \left(\frac{M}{L}\right) \times g \times (L - x) \]

5. **Final Expression for Tension**:
- Thus, the tension in the chain at a distance \( x \) from the rigid support is given by:
\[ T = \frac{M \cdot g \cdot (L - x)}{L} \]

### Summary:
The tension in the chain at a distance \( x \) from the rigid support is:
\[ T = \frac{M \cdot g \cdot (L - x)}{L} \]