A thin bar of length L has a mass per unit length `lambda`, that increases linerarly 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

Options

A. `(L)/(2)-(lambda_(@)L^(2))/(4M)`
B. `(L)/(3)+(lambda_(@)L^(2))/(8M)`
C. `(L)/(3)+(lambda_(@)L^(2))/(4M)`
D. `(2L)/(3)-(lambda_(@)L^(2))/(6M)`

Answer

C