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Q.

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

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a

aL3+bL3

b

12aL2+bL3

c

aL22+bL33

d

12aL22+bL33

answer is C.

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Detailed Solution

Work done in stretching the rubber-band by a distance dx is dW = Fdx = (ax + bx2)dx

Integrating both sides, W=∫0Laxdx+∫0Lbx2dx = aL22+bL33

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