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When a rubber-band is stretched by a dis...

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 unstretched rubber band by L is :

A

`1/2 ((aL^(2))/(2)+(bL^3)/(3))`

B

`aL^(2)+bL^(3)`

C

`(1)/(2)(aL^(2)+bL^(2))`

D

`(aL^(2))/(2) +(bL^3)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
d
Here,`work done = force xx distance`
Now `F=ax+bx^2`
`:. dW=Fdx=int_o^L(ax+bx^2)dx=(aL^2)/(2)+(bL^3)/(3)`.
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