A. `(3(2+b))/(4(3b+b))`
B. `(4(2+b))/(3(3+b))`
C. `(3(3+b))/(4(2+b))`
D. `(4(3+b))/(3(2b+b))`
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Correct Answer – A
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.