If a spring extends by `x` on loading, then the energy stored by the spring is (if T is tension in the spring and k is spring constant)

Options

A. `(T^2)/(2x)`
B. `(T^2)/(2k)`
C. `(2x)/(T^2)`
D. `(2T^2)/(k)`

Explanation

To find the energy stored in a spring when it extends by `x` under a load, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Energy Stored in a Spring**:
The energy (U) stored in a spring when it is extended by a distance `x` is given by the formula:
\[ U = \frac{1}{2} k x^2 \]
where `k` is the spring constant.

2. **Relate Tension and Spring Constant**:
When a spring is stretched, the tension (T) in the spring is related to the spring constant (k) and the extension (x) by Hooke's Law:
\[ T = kx \]
From this, we can express `x` in terms of `T` and `k`:
\[ x = \frac{T}{k} \]

3. **Substitute x in the Energy Formula**:
Now, substitute the expression for `x` into the energy formula:
\[ U = \frac{1}{2} k \left(\frac{T}{k}\right)^2 \]

4. **Simplify the Expression**:
Simplifying the equation:
\[ U = \frac{1}{2} k \cdot \frac{T^2}{k^2} \]
\[ U = \frac{1}{2} \cdot \frac{T^2}{k} \]

5. **Final Expression for Energy Stored**:
Thus, the energy stored in the spring can be expressed as:
\[ U = \frac{T^2}{2k} \]

### Conclusion:
The energy stored by the spring when it extends by `x` under a load T is:
\[ U = \frac{T^2}{2k} \]