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

The
dimension of G can be found by the formula F=Gm

_{1}m_{2}/r^{2}
i.e.
G=F r

^{2}/ m_{1}m_{2 }__Dimensions:__[F]=MLT

^{-2 }[r]=L [m]=M

So
[G] = MLT

^{-2}L^{2}M^{-2}=M^{-1}L^{3}T^{-2}
Now,
the dimension of g is given by

[g]=LT

^{-1}
Now,
finding the ratio of G to g;

ð
M

^{-1}L^{3}T^{-2}/ LT^{-1}
ð
M

^{-1}L^{2}T^{-1 }
Hence it is the ratio of dimensions
of G to the dimensions of g.

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