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. angle
B. length
C. mass
D. None of these

Explanation

`[E]=[ML^(2)T^(-2)]`
`[M]=[M],[L]=[ML^(2)T^(-1)]` ltbr. `[G]=[M^(-1)L^(3)T^(-2)]`
`[(E^(2)L^(2)]/(M^(5)G^(2))]=([ML^(2)T^(-2)]^(2)[ML.^(2)T^(-1)]^(2))/([M]^(5)[M^(-1)L^(3)T^(-2)]^(2))`
`=([M^(2)L^(4)T^(-4)][M^(2)L^(4)T^(-2)])/([M^(5)][M^(-2)L^(6)T^(-4)])=([M^(4)L^(8)T^(-6)])/([M^(3)L^(6)T^(-4)])=[ML^(2)T^(-2)]`
The quantity `((E^(2)L^(2))/(M^(5)G^(2)))` hs the dimensions of
energy.
None of the given option is correct.
If the quantity `(EL^(2))/(M^(5)G^(2)))` is given in place of quantity
`((E^(2)L^(2))/(M^(5)G^(2)))` , then the option (1) is correct.
`[(EL^(2))/(M^(5)G^(2))]=([ML^(2)T^(-2)][ML^(2)T^(-1)]^(2))/([M^(5)][M^(-1)L^(3)T^(-2)]^(2))`
`=([ML^(2)T^(-2)][M^(2)L^(4)T^(-2)])/([M^(5)[M^(-2)L^(6)T^(-4)])]=([M^(3)L^(6)T^(-4)])/([M^(3)L^(6)T^(-4)])`
`[M^(0)L^(0)T^(0)]= "Angle"`