Q 1686523477.     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 2014 Mains Paper - 3
A

`\frac{L}{2} - \frac{\lambda_0 L^2}{4M}`

B

`frac{L}{3} + \frac{\lambda_0 L^2}{4M}`

C

`frac{L}{3} + \frac{\lambda_0 L^2}{8M}`

D

`frac{2L}{3} - \frac{\lambda_0 L^2}{6M}`

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