1.

If E, M, J and G respectively denote energy, mass angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimensions of (EJ^(2))/(M^(5)G^(2))

Answer»

Time
Angle
Mass
Length

Solution :The DIMENSIONAL formulae are,
` E = [ML^(2)T^(-2)], J = [ML^(2)T^(-1)], M = [M], G = [M^(-1)L^(3)T^(-2)]`
On subtituting above formulae in `EJ^(2)/M^(5)G^(2)`,
`EJ^(2)/M^(5)G^(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)` = Dimensionless


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