The ratio of the dimensions of G to those of g is..... ?

The dimension of G can be found by the formula F=Gm₁m₂/r²

i.e. G=F r²/ m₁m₂      

Dimensions: [F]=MLT^-2         [r]=L               [m]=M

So [G] = MLT^-2 L²M^-2=M^-1L³T^-2

Now, the dimension of g is given by

[g]=LT^-2

Now, finding the ratio of G to g;

ð M^-1L³T^-2/ LT^-2

ð M^-1 L² 

Hence it is the ratio of dimensions of G to the dimensions of g.