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Question

A spring with force constant k is initially stretched by x1. If it further stretched by x2, then the increase in its potential energy is

A
12k(x2x1)2
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B
12kx2(x2+2x1)
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C
12 kx21+12 kx22
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D
12 k(x1+x2)2
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E
12 k(x1+x2)3
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Solution

The correct option is B 12kx2(x2+2x1)
According to the question, in the first condition
U1=12kx21....(i)
In the second condition,
U2=12k(x1+x2)2....(ii)
Increment in the potential energy
=U2U1
=12k(x21+x22+2x1x2)12kx21
=12k(x21+x22+2x1x2x21)
=12k[2x1x2+x22]
=12kx2(x1+2x1).

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