(a) State the mathematical relationship that gives the gravitational force F between two point masses.
(b) Explain, without performing any numerical calculation, what happens to the magnitude of F in each of the following independent situations:
(i) both masses are doubled while the separation remains unchanged,
(ii) the separation between the masses is doubled while their masses remain unchanged,
(iii) one mass is doubled, the other is halved and the separation is halved.
(c) A student plots logF on the y-axis against logr on the x-axis for several pairs of identical spheres. Describe the qualitative shape of the graph and justify the numerical value of its slope.
(d) The student claims that the slope obtained in part (c) is independent of the actual values of the two masses chosen. Give a reasoned argument to support or refute this claim.