The density of a rod of 1 m and of non-uniform structure is given by `rho(x)=a(1+bx^(2))`,
where a and b are constant such that `alexle1`. 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])/(4[2+b])`
D. `(4[3+b])/(3[2+b])`

Answer

A

Explanation

Here `rho(x)=1+bx^(2)`. Now `rho` will be constant when `b=0`, otherwise it will be dependent on .x.. The centre of mass is at `x=0.5` m for uniform density of the rod.