A heavy weight is suspended from a spring . A person raises the weight till the spring becomes slack . The done by him is `W`. The energy storeed in the stretched spring was `E` . What will be the gain in gravitational potential energy?

Options

A. `W`
B. `E`
C. `W + E`
D. `W - E`

Explanation

To solve the problem, we need to analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- A heavy weight is suspended from a spring. When the person raises the weight, the spring stretches and stores potential energy until the spring becomes slack.

2. **Identifying Work Done**:
- The work done by the person in raising the weight is given as \( W \).

3. **Energy Stored in the Spring**:
- The energy stored in the stretched spring when it is at maximum stretch is given as \( E \).

4. **Conservation of Energy Principle**:
- According to the conservation of energy, the total work done on the system must equal the change in energy forms. In this case, the work done by the person goes into increasing the gravitational potential energy of the weight and the energy stored in the spring.

5. **Gain in Gravitational Potential Energy**:
- The gravitational potential energy gained by the weight when it is raised to a height \( H \) can be expressed as:
\[ \text{Gain in Gravitational Potential Energy} = \text{Work Done by the Person} + \text{Energy Stored in the Spring} \]
- Therefore, we can write:
\[ \Delta U = W + E \]
- Here, \( \Delta U \) represents the gain in gravitational potential energy.

6. **Final Result**:
- The gain in gravitational potential energy is:
\[ \Delta U = W + E \]

### Conclusion:
The gain in gravitational potential energy when the weight is raised until the spring becomes slack is \( W + E \).

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