Answer:
[tex]M^{-1}L^{3}T^{-2}[/tex]
Explanation:
Force has the unit N for Newton.
A Newton is [tex]m*\frac{kg}{s^{2} }[/tex] , mass*kilograms/seconds^2.
Dimensions in Physics include things such as Mass, Length, and Time.
kg is Mass
m is Length
s^2 is Time
So, since a Newton has all of these, it has T, L, and M. Force has dimensions [tex]T^{-2}LM[/tex]
However, you must now consider gravitational force.
Law of Gravitation states:
[tex]F=\frac{Gm_{1}m_{2}r }{r^{2} }[/tex]
Convert that into a fraction with dimensions:
[tex]F=\frac{GM^{2} L}{L^{2} }[/tex]
Remember force is [tex]T^{-2}LM[/tex]
Use the dimensions of force to find gravitational force, or G:
[tex]F=\frac{GM^{2} L}{L^{2} }[/tex]
[tex]T^{-2}LM=\frac{GM^{2} L}{L^{3} }[/tex]
[tex]G=\frac{(T^{-2}LM)(L^{2}) }{M*M}[/tex]
[tex]G=\frac{(T^{-2}L^{3} M) }{M^{2} }[/tex]
[tex]G=M^{-1}L^{3}T^{-2}[/tex]
