The centre of mass of a, non uniform rod of length L whose mass per unit length p varies as p =`(kx^(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/8
C. `(k)/(L)`
D. `(3k)/(L)`

Explanation

`COM=(int_(0)^(L)x(dm))/(int_(0)^(L)dm)=(int_(0)^(L)x((kx^(2))/(L))(dx))/(int_(0)^(L)(kx^(2))/(L)(dx))=(k((L^(4))/(4)))/(k((L^(3))/(3)))=(3L)/(4)`