If the orbital velocity of a planet is given by `v = G^(a) M^(b) R^(c )` then

Options

A. `a=(1)/(2), b=(1)/(2), c =-(1)/(2)`
B. `a=(1)/(2), b= -(1)/(2), c = (1)/(2)`
C. `a=(1)/(2), b=-(1)/(2), c=-(1)/(2)`
D. `a=(1)/(3), b = (1)/(3), c = - (1)/(3)`

Answer

A

Explanation

The orbital velocity of a planet is given by
`v = sqrt((GM)/(R ))=G^(1//2)M^(1//2)R^(-1//2)`
Comparing this with `v = G^(a)M^(b)R^(c )` we get
`a=(1)/(2), b=(1)/(2)` and `c = -(1)/(2)`