If E= energy, G= gravitational constant, I= impulse and M= mass, then dimensions of G I M^2 E^2 are same as that of

Step-by-step solution

The SI unit in which G is measured = N - m ^2 / kg ^2 Its dimensions will be [ MLT ⁻² ] [ L ^2 ] [ M ^2 ] = [ M ⁻¹ ~L ^3 ~T ⁻² ] Impulse = Force Time = [ MLT ⁻² ][ T ]= [ MLT ⁻¹ ] Dimensions for energy = [ ML ^2 ~T ⁻² ] Now put the dimensions of G, I, M and E in G I M^2 E^2 aligned & = [ M ⁻¹ ~L ^3 ~T ⁻² ] [ MLT ⁻¹ ] [ M ^2 ] [ ML ^2 ~T ⁻² ]^2 & = [ M ⁻¹ ~L ^3 ~T ⁻² ] [M L T⁻¹ ] [ M ^2 ] [ M ^2 ~L ^4 ~T ⁻⁴ ] = [ M ^2 ~L ^4 ~T ⁻³ ] [ M ^2 ~L ^4 ~T ⁻⁴ ] & = [ T ⁻¹ ]=[T] aligned The equation G I M^2 E^2 has dimension