The centre of mass of a non uniform rod of length L, whose mass per unit length varies as `rho=(k.x^2)/(L)` where k is a constant and x is the distance of any point from one end is (from the same end)

Options

A. `3L//4`
B. `L//4`
C. `2L//3`
D. `L//3`

Answer

A

Explanation

`bar(x) = (intxdm)/(intdm) = (int_(0)^(L) x(kx^(2))/(L)dx)/(int(kx^(2))/(L)dx) = (3L)/(4)`