Force–displacement $(F - x)$ graphs for four different particles moving along a straight line are shown. If $W_{1}, W_{2}, W_{3} a n d W_{4}$ are the works done corresponding to figures a, b, c and d respectively, then $(x_{0} = x_{1} - x_{0} = x_{2} - x_{1} = x_{3} - x_{2})$
a) b)
c) d)

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$W_{3} > W_{2} > W_{1} > W_{4}$

$W_{3} > W_{2} > W_{4} > W_{1}$

$W_{2} > W_{3} > W_{4} > W_{1}$

$W_{2} > W_{3} > W_{1} > W_{4}$

answer is A.

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Detailed Solution

From the graph,
Work done = Area under F – X curve.
Also, area below X-axis is negative & area above X-axis is positive.
From the given graph, it is clearly visible that,
$A_{3} > A_{2} > A_{1} > A_{4}$

$∴ W_{3} > W_{2} > W_{1} > W_{4} {∵ W α A; A = a r e a}$

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