Work Energy Power

JEE Main level, single correct, medium

28 of 183

Question 28 of 183

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 :

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Answer: (C) aL22+bL33\dfrac{{\text{aL}}^{2}}{2}+\dfrac{{\text{bL}}^{3}}{3}

W=∫Fdx\text{W}=\int \text{F}\text{d}\text{x}

=∫(ax+bx2)dx=\int \left(\text{ax}+{\text{bx}}^{2}\right)\text{dx}

=a2[x2]0L+b3[x3]0L=\dfrac{\text{a}}{2}{\left[{\text{x}}^{2}\right]}_{0}^{\text{L}}+\dfrac{\text{b}}{3}{\left[{\text{x}}^{3}\right]}_{0}^{\text{L}}

=aL22+bL33=\dfrac{\text{a}{\text{L}}^{2}}{2}+\dfrac{\text{b}{\text{L}}^{3}}{3}

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