Work Power and Energy 1 Question 3

4. 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

(2014 Main)

(a) aL2+bL3

(b) 12(aL2+bL3)

(c) aL22+bL33

(d) 12aL22+bL33

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Answer:

Correct Answer: 4. (c)

Solution:

  1. Thinking Process We know that change in potential energy of a system corresponding to a conservative internal force as

UfUi=W=ifFdr

Given,

F=ax+bx2

We know that work done in stretching the rubber band by L is |dW|=|Fdx|

|W|=0L(ax+bx2)dx=ax22L+bx330=aL22a×(0)22+b×L33b×(0)33=|W|=aL22+bL33



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