A particle is displaced from point P(3 m, 4 m, 5 m) to a point Q(2 m, 3 m, 4 m) under a constant force F = (3i + 4j + 5k) N. The work done by the force in this process is (a) +10 J (b) +4 J (c) -8 J (d) -12 J

Answer: (d). W = F with s = rQ - rP. s = (2-3)i + (3-4)j + (4-5)k = -i - j - k m W = 3(-1) + 4(-1) + 5(-1) = -12 J So the answer is (d) -12 J.

A particle is displaced from point P(3 m, 4 m, 5 m) to a point Q(2 m… | MHT CET 2025 (23 Apr, Shift 2)

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Work by a Constant Force

A particle is displaced from point $P(3\text{ m}, 4\text{ m}, 5\text{ m})$ to a point $Q(2\text{ m}, 3\text{ m}, 4\text{ m})$ under a constant force $\vec{F} = (3\hat{i} + 4\hat{j} + 5\hat{k})\text{ N}$ . The work done by the force in this process is

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Answer: (d)

$W = \vec{F}\cdot\vec{s}$ with $\vec{s} = \vec{r}_Q - \vec{r}_P$ .
$\vec{s} = (2-3)\hat{i} + (3-4)\hat{j} + (4-5)\hat{k} = -\hat{i} - \hat{j} - \hat{k}$ m
$W = 3(-1) + 4(-1) + 5(-1) = -12$ J
So the answer is (d) $-12$ J.

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