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Assertion :- Work done is positive when ...

Assertion `:-` Work done is positive when force acts in the direction of displacement.
Reason `:-` Work done by frictional force can not be positive.

A

If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion.

B

If both Assertion & Reason are True but Reason is not a correct explanation of the Assertiion.

C

If Assertion is True but the Reason is False.

D

If both Assertion & Reason are False

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The correct Answer is:
To analyze the assertion and reason provided in the question, we can break down the concepts of work done, force, and displacement step by step. ### Step-by-Step Solution: 1. **Understanding Work Done**: - Work done (W) by a force is defined as the dot product of the force (F) and the displacement (S) of the object. Mathematically, it can be expressed as: \[ W = \vec{F} \cdot \vec{S} = F \cdot S \cdot \cos(\theta) \] - Here, \(\theta\) is the angle between the force vector and the displacement vector. 2. **Positive Work Done**: - Work done is considered positive when the force acts in the same direction as the displacement. This occurs when \(\theta = 0^\circ\), leading to: \[ W = F \cdot S \cdot \cos(0) = F \cdot S \cdot 1 = F \cdot S \] - Therefore, the assertion that "Work done is positive when force acts in the direction of displacement" is **true**. 3. **Frictional Force and Work Done**: - The reason states that "Work done by frictional force cannot be positive." - Frictional force typically acts opposite to the direction of displacement. When an object moves, the frictional force does negative work because it opposes the motion. This can be expressed as: \[ W_{\text{friction}} = F_{\text{friction}} \cdot S \cdot \cos(180^\circ) = -F_{\text{friction}} \cdot S \] - Thus, the work done by friction is negative when it opposes the motion. 4. **Counterexamples**: - However, there are scenarios where friction can do positive work. For example, when a car accelerates, the frictional force between the tires and the road acts in the direction of the car's displacement, contributing positively to the car's acceleration. - Hence, the statement that "Work done by frictional force cannot be positive" is **false**. 5. **Conclusion**: - The assertion is true, while the reason is false. Therefore, the overall conclusion is that the assertion is correct, but the reason provided is incorrect. ### Final Answer: - Assertion: True - Reason: False
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