Two point masses m1 and m2 are separated by a distance r. Answer the following with reference to the gravitational force F acting between them.
(i) Write the mathematical relationship connecting F and r.
(ii) On the same set of axes, sketch qualitatively (no scale needed) the graphs of (a) F versus r and (b) F versus r21. Label the curves clearly.
(iii) Explain why the F versus r curve approaches, but never meets, either axis even when extended indefinitely.
(iv) Using your sketch, state how the force changes when the separation between the masses is doubled. Justify your answer without using numerical calculation.