A thin bar of length $\mathrm{L}$ has a mass per unit length $\lambda$, that increases linearly with…

A thin bar of length $\mathrm{L}$ 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. $\frac{2 \mathrm{~L}}{3}-\frac{\lambda_0 \mathrm{~L}^2}{6 \mathrm{M}}$

Solution

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Asked in: JEE Main 2014 (11 Apr Online)

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