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

Answer

A

Explanation

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