The period `T_0` for a planet of mass 'm' above the sum in a circular orbit of radius R depends on m,R and G where G is the gravitational constant. Find expression for time period by dimensional methods.

Explanation

`T_(0)prop m^(a)R^(b)g^©,mrarrM, R rarrL, Grarr M^(-1)L^(3)T^(-2), T_(0)rarrT :. T^(1) = K(M)^(a)(L)^(b)(m^(-1)L^(3)T^(-(2))^(C) )` comparing powers of M,L and T on either sides
`a-c=0` ….(1)
`b=3c=0 …(2)
`2c=1rArr c=-1/2`
`:. B=3/2and a=-1/2 :. T_(0)=Km^(1/2)R^(3/2)G^(-1/2), T_(0)=KsqrtR^(3)/(GM)`