Assertion : For two bodies , the sum of the mutual forces exerted between them is zero from Newton's third law. Reason : The sum of work done by the two forces must always cancel.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true not but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false
D. If both assertion and reason are false.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Analyze the Assertion
The assertion states that for two bodies, the sum of the mutual forces exerted between them is zero according to Newton's third law.

**Explanation**:
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that if body A exerts a force \( F_{AB} \) on body B, then body B exerts a force \( F_{BA} \) on body A such that:
\[ F_{AB} + F_{BA} = 0 \]
This implies that the forces are equal in magnitude and opposite in direction. Therefore, the assertion is **correct**.

### Step 2: Analyze the Reason
The reason states that the sum of work done by the two forces must always cancel.

**Explanation**:
Work done is defined as the product of force and displacement in the direction of the force. If we have two forces \( F_1 \) and \( F_2 \) acting on a body with displacements \( S_1 \) and \( S_2 \) respectively, the work done by these forces can be expressed as:
\[ W_1 = F_1 \cdot S_1 \]
\[ W_2 = -F_2 \cdot S_2 \]
The total work done \( W \) is:
\[ W = W_1 + W_2 = F_1 \cdot S_1 - F_2 \cdot S_2 \]
This does not necessarily equal zero unless specific conditions are met (e.g., equal displacements in opposite directions). Therefore, the reason is **incorrect**.

### Conclusion
- Assertion: True
- Reason: False

Thus, the correct answer is that the assertion is true, but the reason is false.

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