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A body is displaced from $x = 4 m$ to $x = 2 m$ along the x-axis. For the forces mentioned in Column-I, match the corresponding work done is Column-II.
Column-I Column-II
A $F = 4 \hat{i}$ P positive
B $F = (4 \hat{i} - 4 \hat{j})$ Q negative
C $F = - 4 \hat{i}$ R zero
D $F = (- 4 \hat{i} - 4 \hat{j})$ S $| W | = 8$ units

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$A - Q S, B - Q S, C - P S, D - P R$

$A - Q S, B - Q S, C - P S, D - P S$

$A - P S, B - Q S, C - P S, D - P S$

$A - Q S, B - P S, C - P S, D - P R$

answer is B.

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Detailed Solution

Workdone is given as

$W = \vec{F} . \vec{d x}$

Here

$\vec{d x} = - 2 \hat{i}$

A) $W = (4 \hat{i}) . (- 2 \hat{i}) = - 8 u n i t s$

B) $W = (4 \hat{i} - 4 \hat{j}) . (- 2 \hat{i}) = - 8 u n i t s$

C) $W = (- 4 \hat{i}) . (- 2 \hat{i}) = 8 u n i t s$

D) $W = (- 4 \hat{i} - 4 \hat{j}) (- 2 \hat{i}) = 8 u n i t s$

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