The centre of mass of a non uniform rod of length L, whose mass per unit length varies as `rho=(k.x^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. `(3/4)L`
B. `(1/4)L`
C. `(1/6)L`
D. `(2/3)L`

Answer

A

Explanation

`dm=("Mass per unit length")("Length")
`=((kx^(2))/(L))dximpliesX_(COM)=(int_(0)^(L)xdm)/(int_(0)^(L)dm)`
`=(int_(0)^(L)(x)((kx^(2))/(L))dx)/(int_(0)^(L)((kx^(2))/(L))dx)=3/4L`