To solve this problem, we need to determine the dimensions of $\frac{E}{G}. \\$First, let's recall the dimensions of energy $E$ and the gravitational constant $G. \\$• Energy $E$ is typically measured in joules (J), which has the dimensions:$\\ E = [M L^2 T^{-2}] \\$• The gravitational constant $G$ has the dimensions:$\\ G = [M^{-1} L^3 T^{-2}] \\$Now, we need to find the dimensions of $\frac{E}{G}. \\$Substitute the dimensions of $E$ and $G: \\ \frac{E}{G} = \frac{[M L^2 T^{-2}]}{[M^{-1} L^3 T^{-2}]} \\$Simplify the expression by dividing the dimensions:$\\ \frac{E}{G} = [M L^2 T^{-2}] \times [M L^{-3} T^2] \\$Combine the dimensions:$\\ \frac{E}{G} = [M^{1+1} L^{2-3} T^{-2+2}] \\ \frac{E}{G} = [M^2 L^{-1} T^0] \\$Thus, the dimensions of $\frac{E}{G}$ are $[M^2 L^{-1} T^0]. \\$This corresponds to Option 1.