The centre of mass of a non uniform rod of length `L` whoose mass per unit length varies as `p=kx^(2)//L`, (where `k` is a constant and `x` is the distance measured form one end) is at the following distances 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)`