The linear density of a non`-`uniform rod of length `2m` is given by `lamda(x)=a(1+bx^(2))` where `a` and `b` are constants and `0lt=xlt=2`. The centre of mass of the rod will be at. `X=`

Options

A. `(3+6b)/(6+8b)`
B. `(6+2b)/(3+4b)`
C. `(3+6b)/(3+4b)`
D. `(1+2b)/(3+4b)`

Answer

C

Explanation

Ans. (3)
`(int_(0)^(2)a(1+bx)^(2)xdx)/(int_(0)^(2)a(1+bx^(2))dx)=((3+6b))/((3+4b))`