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

Question:

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

1. $\mathrm{aL}^{2}+\mathrm{bL}^{3}$

2. $\frac{1}{2}\left(a L^{2}+b L^{3}\right)$

3. $\frac{\mathrm{aL}^{2}}{2}+\frac{\mathrm{bL}^{3}}{3}$

4. $\frac{1}{2}\left(\frac{\mathrm{aL}^{2}}{2}+\frac{\mathrm{bL}^{3}}{3}\right)$

JEE Main Previous Year Single Correct Question of JEE Main from Physics Work, Energy and Power chapter.

JEE Main Previous Year 2014

Correct Option: 3

Solution: