the density of a non-uniform rod of length 1 m is given by `rho(x)=a(1+bx^(2))` where ,a and b are constants and `0lexle1,` the centre of mass of the rod will be at.

Answer

A

Explanation

Density is given as `rho (x) = a (1+bx^(2))`
where a and b are constants and `0 le x le 1`
Let `b rarr 0`, in this case
`rho (x) = a=` constant
Hence, centre of mass will be at `x=0.5` m (middle of the rod) Putting, `b=0` in all the options, only (a) given 0.5.
Note : We should not check options by putting `a=0`, because `rho = 0` for a = 0.