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Physics

Assertion (A) : When the displacement is zero, then the work is zero. So, if the work done is zero, then it necessarily means the displacement is zero.

Reason(R) : Work done is calculated by the relation š‘Š=š¹š‘† š‘š‘œš‘  šœƒ

  1. A and R are true, and R is the reason for A.
  2. A and R are true, and R is not the reason for A.
  3. A is true, but R is false.
  4. A is false, but R is true.

Work, Energy & Power

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Answer

A is false, but R is true.

Explanation :
Work is given by Wāƒ—=Fāƒ—ā‹…Sāƒ—W=FScos⁔θ\vec{W} = \vec{F} \cdot \vec{S} \\[1em] W = F S \cos\theta so the reason is correct.

But zero work doesn't always mean zero displacement. For example, when force is perpendicular to displacement (like carrying a bag horizontally). Here, the angle between force and displacement is 90° so work done ∣Wāƒ—āˆ£=∣Fāƒ—āˆ£āˆ£Sāƒ—āˆ£cos⁔90°=0|\vec{W}| = |\vec{F}||\vec{S}| \cos 90°= 0 \\[1em] work is still zero, even though displacement exists. Therefore, the reason is correct, but the assertion is not.

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