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 upstretched rubber band by L is

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

Answer 1

The correct option is C

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

Work done is given by $W=\int Fdx=\int (ax+b{x}^2)dx$.
Integrating from $x=0$ to $x=L$, we get $W=\frac{a{L}^2}{2}+\frac{b{L}^3}{3}$.