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. `(2)/(3)L`
B. `(3)/(2)L`
C. `(1)/(2)L`
D. `(4)/(3)L`

Answer

A

Explanation

`X_(cm)=int_(0)^(L)((dm)x)/(int_(0)^(L)(dm))=(int_(0)^(L)(lambdaxdx)x)/(int_(0)^(L)(lambdaxdx))=(2L)/(3)`