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Question

When a rubber band is stretched by a distance x, it exerts a restoring force of magnitude F=ax+bx2, where a and b are constants. The work done in stretching the upstretched rubber band by L is


A

aL2+bL3

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B

12(aL2+bL3)

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C

aL22+bL33

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D

12(aL22+bL33)

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Solution

The correct option is C

aL22+bL33


Work done is given by W=Fdx=(ax+bx2)dx.
Integrating from x=0 to x=L, we get W=aL22+bL33.


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