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 E J^2 M^5 G^2

Step-by-step solution

Given quantity is E J^2 M^5 G^2 where dimensions of the various given quantities are Dimensions of E= [ ML ^2 ~T ⁻² ] Dimensions of J= [ ML ^2 ~T ⁻¹ ] Dimension of M=[ M ] Dimension of G= [ M ⁻¹ ~L ^3 ~T ⁻² ] Now, on putting these dimensions in Eq. (i), we have aligned & = [ ML ^2 ~T ⁻² ] [ ML ^2 ~T ⁻¹ ]^2 [ M ^5 ] [ M ⁻¹ ~L ^3 ~T ⁻² ]^2 & = [ M ^3 ~L ^6 ~T ⁻² ] [ M ^3 ~L ^6 ~T ⁻² ] = dimensionless aligned Since, angle is a dimensionless quantity