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

Options

A. `(3(a+b))/(4(3+b))`
B. ` (4(a+b))/(3(3+b))`
C. `(3(a+b))/(4(2+b))`
D. `(4(3+b))/(3(2+b))`

Answer

A

Explanation

When `b to 0 ` , the density becomes uniform and hence the centre of mass is at `x = 0.5` .Only option (a) tends to 0.5 `b to 0 `