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.

The period T_0 for a planet of mass 'm' above the sum in a circular or

1.	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.
Answer» SOLUTION :`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)`