Mass is non-uniformly distributed over the rod of length l, its linear mass density varies linearly with length as `lamda=kx^(2)`. The position of centre of mass (from lighter end) is given by-

Options

A. 2l/5
B. 3/l
C. 3l/4
D. 2l/3

Answer

C

Explanation

`X_(cm) = (int x dm)/(int dm)`
`X_(cm) = (int_(0)^(1) x (kx^(2)dx))/(int_(0)^(1) kx^(2) dx)`
`X_(cm) = (l^(4)//4)/(l^(3)//3) = 3/4 l`