Question

Gravitational force acting between two bodies of mass m1 and m2 having a separation r is given by F=G*m1m2/r 2 .obtain the dimension of G.

Answer 1

Force=mass * acceleration
[Force]=[MLT⁻²]
[m₁]=[m₂]=[M]
[r]=[L]
Now putting this value in the given equation, we get-
      [MLT⁻²] = [G]*[M²] / [L²]
==>[G]= [MLT⁻²]*[L²] / [M²]
           =[M⁻¹L³T⁻²]  
This is the required dimension of G.
Hope this helps! :)