The mass per unit length of a non-uniform rod of length L is given by `mu= lamdaxx2`​, where `lamda` is a constant and x is distance from one end of the rod. The distance of the center of mass of rod from this end is :-

Options

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

Answer

C

Explanation

`dm = mu dx = lamda x^(2)dx`
`x_(c.m) =(int xdm)/(int dm)=(underset(0)overset(L)int x lamda x^(2)dx)/( underset(0) overset(L)int lamdax^(2)dx)`
` (|(x^(4))/(4)|_(0)^(L))/(|(x^(3))/(3)|_(0)^(L))=((L^(4))/(4))/((L^(3))/(3))=(3L)/(4)`