QJEEM14Ph6d8f: JEE Main 2014 Physics - Class 11 JEEM14Ph6d8f Solution: When a rubber-band is stretched by a distance x , it exerts…

Question

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When a rubber-band is stretched by a distance

x

, it exerts restoring force of magnitude

F = a x + b x^{2}

where

a

and

b

are constants. The work done in stretching the unstretched rubber-band by

L

is :

Accepted Answer

Given Restoring force, F = ax + bx²

Work done in stretching the rubber-band by a distance

d x

is

d W = F d x = (a x + b x^{2}) d x

Intergrating both sides,

W = \int_{0}^{L} a x d x + \int_{0}^{L} b x^{2} d x

=

{[a \frac{x^{2}}{2} + b \frac{x^{3}}{3}]}_{0}^{L}

=

\frac{a L^{2}}{2} + \frac{b L^{3}}{3}

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