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Question

A block of mass 5 kg is moving in x direction with a constant speed of 20 m/s. It is subjected to a retarding force of F=0.1x joules/metre during its travel from x=20 m to x=30 m. Its final K.E. will be:

A
975 J
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B
1025 J
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C
825 J
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D
725 J
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Solution

The correct option is A 975 J
Since the block is moving under the action of a variable force, work done by the force for displacement from x=20 m to x=30 m is given by
W=xfxiFdx=3020(0.1x)dx
W=0.1[x22]3020=0.12[(30)2(20)2]
W=25 joules

Now, initial kinetic energy KEi=12mu2
KEi=12×5×(20)2=1000 J
Let KEf be the final kinetic energy.
Applying work energy theorem on the block:
Wext=ΔKE
W=KEfKEi
25=KEf1000
KEf=100025=975 J

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