A thin bar of length L has a mass per unit length $\lambda$, that increases linearly with distance from one end. If its total mass is $M$ and its mass per unit length at the lighter end is $\lambda_\mathrm{O}$, then the distance of the centre of mass from the lighter end is:
(1) $\frac{\mathrm{L}}{2} - \frac{\lambda_0 \mathrm{~L}^2}{4\mathrm{M}}$
(2) $\frac{\mathrm{L}}{3} + \frac{\lambda_0 \mathrm{~L}^2}{8\mathrm{M}}$
(3) $\frac{\mathrm{L}}{3} + \frac{\lambda_0 \mathrm{~L}^2}{4\mathrm{M}}$
(4) $\frac{2\mathrm{~L}}{3} - \frac{\lambda_0 \mathrm{~L}^2}{6\mathrm{M}}$