Find the which of the following are correct using dimensional analysis. (i) t^(2)=4pi^(2)a^(3) (ii) t^(2)=(4pi^(2)a^(3))/G (iii) t^(2)=(4pi^(2)a^(3))/(GM) where t is the time period, a is the radius of the orbit of a planet and M is the mass of sun.

Find the which of the following are correct using dimensional analysis

1.	Find the which of the following are correct using dimensional analysis. (i) t^(2)=4pi^(2)a^(3) (ii) t^(2)=(4pi^(2)a^(3))/G (iii) t^(2)=(4pi^(2)a^(3))/(GM) where t is the time period, a is the radius of the orbit of a planet and M is the mass of sun.
Answer» Solution :(i) `r^(2)to[T^(2)],a^(3)to[L^(3)]` not correct (ii) `a^(3)//GTO[L^(3)//M^(-1)L^(3)T^(-2)]=[M^(1)T^(2)]` This equation is not correct (iii) `a^(3)//GMtoL^(3)//M^(-1)L^(3)T^(-2)M=[T^(2)]`. This equation is correct.