Two identical point masses of mass are fixed on the -axis at positions and
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Two identical point masses of mass M are fixed on the x-axis at positions (−d/2,0) and (d/2,0). A small test mass m is placed on the positive y-axis at the coordinate (0,y), where y>0.
Air resistance and all other forces are negligible.
(a) Derive an exact expression for the magnitude of the net gravitational force on the test mass m in terms of G, M, m, d, and y.
(b) State the direction of the net force in vector form, using unit vectors of your chosen coordinate system.
(c) Show algebraically that when y≫d the magnitude of the net force approaches the force that would be produced by a single mass of 2M located at the origin. Clearly indicate any approximations made.
(d) Briefly interpret the physical meaning of the limiting result obtained in part (c).