If `E , M , J , and G` , respectively , denote energy , mass , angular momentum , and gravitational constant , then `EJ^(2) //M^(5) G^(2)` has the dimensions of

Options

A. Length
B. Mass
C. Time
D. Angle

Answer

(d)

Explanation

Here, `E = Energy (M^1 L^2 T^(-2)), m = mass (M^1)`
L = angular momentum `= m upsilon r =(ML^2 T^(-1))`
G = gravitational constant `= (M^(-1) L^3 T^(-2))`
`:. (EL^2)/(m^5 G^2) = M^1 L^2 T^(-2)xx(ML^2 T^(-1))^2/(M^5 (M^(-1)L^3 T^(-2))^2)`
`=(M^3 L^6 T^(-4))/(M^3 L^6 T^(-4)) = M^0 L^0 T^0`
which are the dimensios of Angle
`=(arc)/(radius) = M^0 L^0 T^0`