1. When a rubber band is stretched ...
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1. When a rubber band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx, where a and b are constants. The work done in stretching the unstretched rubber band by L is (2014 Main) (a) al? + bĽ (b)(a + b)

JEE/Engineering Exams
Physics
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1. Thinking Process We know that change in potential energy of a system corresponding to a conservative internal force as Given, [ begin{array}{c} U_{f}-U_{i}=-W=-int_{i}^{f} mathrm{F} cdot d mathrm{r} F=a x+b x^{2} end{array} ] We know that work done in stretching the rubber band by ( L ) is ( |d W|=|F d x| ) [ begin{aligned} |W| &=int_{0}^{L}left(a x+b x^{2}right) d x &=left[frac{a x^{2}}{2}right]_{0}^{L}+left[frac{b x^{3}}{3}right]_{0}^{L} &=left[frac{a L^{2}}{2}-frac{a times(0)^{2}}{2}right]+left[frac{b times L^{3}}{3}-frac{b times(0)^{3}}{3}right] &=|W|=frac{a L^{2}}{2}+frac{b L^{3}}{3} end{aligned} ]
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