Find the x coordinate of the centre of mass of the non - uniform rod of length L givne below. The origin is taken at the left end of the rod. The density of the rod as a function of its x- coordinates is `rho=ax^(2)+bx+c`, where a, b and c are constants.

Options

A. `(2aL^(2)+3bL^(2)+6cL)/(2(3aL^(2)+4bL+8c))`
B. `(4aL^(3)+3bL^(2)+2cL)/(2(3aL^(2)+2bL+c))`
C. `(3aL^(2)+4bL^(2)+2cL)/(4aL^(2)+6bL+8c)`
D. `(3aL^(3)+4bL^(2)+6cL)/(2(2aL^(2)+3bL+6c))`

Answer

D