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

The density of a non-uniform rod of length 1m is given by `rho (x)=a (

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

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