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 $\lambda_0$, then the distance of the centre of mass from the lighter end is
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 $\lambda_0$, then the distance of the centre of mass from the lighter end is
- [JEE MAIN 2014]
- A
$\frac{L}{2} - \frac{{{\lambda _0}{L^2}}}{{4M}}$
- B
$\frac{L}{3} + \frac{{{\lambda _0}{L^2}}}{{8M}}$
- C
$\frac{L}{3} + \frac{{{\lambda _0}{L^2}}}{{4M}}$
- D
$\frac{{2L}}{3} - \frac{{{\lambda _0}{L^2}}}{{6M}}$
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