As will be shown in Problem, the magnitude of the tidal force exerted on an object of mass...

As will be shown in Problem, the magnitude of the tidal force exerted on an object of mass m and length a is approximately 4GmMa/r3. In this expression, M is the mass of the body causing the tidal force and r is the distance from the center of m to the center of M. Suppose you are 1 million miles away from a black hole whose mass is a million times that of the Sun. (a) Estimate the tidal force exerted on your body by the black hole. (b) At what distance will the tidal force be approximately 10 times greater than your weight?

Problem

A dumbbell has a mass m on either end of a rod of length 2a. The center of the dumbbell is a distance r from the center of the Earth, and the dumbbell is aligned radially. If r ≥ a, show that the difference in the gravitational force exerted on the two masses by the Earth is approximately 4GmME a/r3. (Note: The difference in force causes a tension in the rod connecting the masses. We refer to this as a tidal force.) [Hint: Use the fact that ]