Question

1. Suppose that the mass of a star and its radius both somehow doubles. Use the equation for
gravitational force to show by what factor the force of gravity changes on its surface.

Answer 1

The force of gravity at the surface of the star

$$F_0=G\frac{M_0m}{R_0^2}.$$

Hence

$$F=G\frac{2M_0m}{(2R_0)^2}=\frac{1}{2}G\frac{M_0m}{R_0^2}=\frac{1}{2}F_0.$$