A straight-line graph is obtained by plotting gravitational force F on the vertical axis against r21 on the horizontal axis for two point masses m1 and m2.
(i) Derive an expression for the slope S of this graph in terms of G, m1 and m2.
(ii) The original slope is S0. Predict the new slope S1 if m1 is made three times larger while m2 is simultaneously reduced to one-half of its original value. Express S1 in terms of S0.
(iii) Explain physically why the shape of the graph remains unchanged even though its slope alters.