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 stored in the stretched spring was `E` . What will be the gain in gravitational potential energy?

Options

A. (a) W
B. (b) E
C. (c) `W+E`
D. (d) `W-E`

Explanation

To solve the problem, we need to analyze the situation involving the work done by a person, the energy stored in the spring, and the gain in gravitational potential energy. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Work Done
The work done by the person, denoted as \( W \), is the energy transferred to the system when the person raises the weight. This work is done against the gravitational force acting on the weight.

**Hint:** Remember that work done is the energy transferred to an object when a force is applied over a distance.

### Step 2: Energy Stored in the Spring
When the weight is raised, the spring gets stretched, and energy is stored in the spring. This energy is denoted as \( E \). The energy stored in the spring is a result of the work done on it as it is stretched.

**Hint:** The energy stored in a spring is given by the formula \( E = \frac{1}{2} k x^2 \), where \( k \) is the spring constant and \( x \) is the extension.

### Step 3: Gain in Gravitational Potential Energy
The gain in gravitational potential energy (GPE) when the weight is raised can be understood as the total energy input into the system. This includes both the work done by the person and the energy stored in the spring.

**Hint:** The gravitational potential energy gained can be thought of as the total energy transferred to the weight as it is lifted.

### Step 4: Combine the Energies
The total gain in gravitational potential energy can be expressed as:
\[ \text{Gain in GPE} = W + E \]
This equation shows that the gain in gravitational potential energy is the sum of the work done by the person and the energy stored in the spring.

**Hint:** When multiple forms of energy are added together, ensure they are all in the same direction and context.

### Step 5: Conclusion
Thus, the gain in gravitational potential energy when the weight is raised until the spring becomes slack is:
\[ \text{Gain in GPE} = W + E \]

**Final Answer:** The correct answer is \( W + E \).