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Question

Figure gives the acceleration of a 2.0 kg body as it moves from rest along x axis, while a variable force acts on it from x=0 m to x=9 m.
The work done by the force on the body when it reaches x=4 m and x=7 m is

A
21 J and 33 J respectively
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B
21 J and 15 J respectively
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C
42 J and 60 J respectively
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D
42 J and 30 J respectively
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Solution

The correct option is D 42 J and 30 J respectively

Here we have acceleration versus displacement graph.
Work done by the force on the body,
when it reaches at x=4 m is
Wt=4 = Mass of the body × Area under ABCD
Wt=4=2[(12×1×6)+(3×6)]=42 J

Work done by the force on the body when it reaches at x=7 m is
Wt=7=Wt=4+ (Mass of the body )(Area under CDE - Area under EFGH)
=42 +2[(12×1×6)(12×1×6)(1×6)]
Wt=7=30 J

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