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

Options

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

Answer

D

Explanation

E `= [ML^(2)T^(-2)]`
`M =[M], L= [ML^(2)T^(-1)]`,
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)))` has the dimensions of energy.
None of the given options is correct.