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 at

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

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 at
Answer» `(3(2+B))/(4(3b+b))` `(4(2+b))/(3(3+b))` `(3(3+b))/(4(2+b))` `(4(3+b))/(3(2b+b))` SOLUTION :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.