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Question

A spring of spring constant 5×103 N/m is stretched initially by 5 cm from the unstretched position. The work required to further stretch the spring by another 5 cm is

A
6.25 J
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B
12.50 J
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C
18.75 J
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D
25.00 J
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Solution

The correct option is C 18.75 J
Given spring constant (k)=5×103 N/m
Spring force (F)=kx (where x is deformation in spring)
Work done by deforming force to stretch the spring from x1=5 cm to x2=10 cm
w=F.ds=x2x1Fxdx=x2x1kx dx=k(x2)2|x2x1=k(x222x212)=12k(x22x21)=12×5×103((10×102)2(5×102)2)=12×5×103×104(10025)=754=18.75 J

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