Question

When a rubber band is stretched by a distance $x$, it exerts a restoring force of magnitude $F=ax+b{x}^2,$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber band by $L$ is

• A. $a{L}^2+b{L}^3$
• B. $\frac{1}{2}(a{L}^2+b{L}^3)$
• C. $\frac{1}{2}(\frac{a{L}^2}{2}+\frac{b{L}^3}{3})$
• D. $\frac{a{L}^2}{2}+\frac{b{L}^3}{3}$

Answer 1

The correct option is D $\frac{a{L}^2}{2}+\frac{b{L}^3}{3}$

Work done is streching the rubber band
$W={\int }_0^L(ax+b{x}^2)dx=\frac{a{L}^2}{2}+\frac{b{L}^3}{3}$