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Question

A spring of unstretched length l and force constant k is stretched by a small length x. It is further stretched by another small length y. The work done in the second stretching is

A
12kx2
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B
12k(x2+y2)
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C
12ky(2x+y)
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D
12kx(x+2y)
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Solution

The correct option is C 12ky(2x+y)
When the spring is stretched by the spring force which is conservative in nature, work done by spring force is
W=ΔU=(UfUi)=UiUf
=12kx2(12k(x+y)2)
=12kx212kx212ky2kxy
=12ky2kxy=12ky(y+2x)
Work done by external agent is negative of this.
Hence, the correct answer is option (c).

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