The magnitude of the tidal force exerted on a linear object of mass m and length L is approximately 2GmML/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 (1.6 × 109 m) away from a black hole whose mass is 1.99 × 1036 kg (one million times that of the Sun).

(a) Estimate the tidal force exerted on your body (L = 1.8 m) by the black hole.

(b) At what distance will the tidal force be approximately 10 times greater than your weight?