Chapter 13, Problem 39A

If you stand on a shrinking planet, so that in effect you get closer to its center, your weight will increase. But if you instead burrow into the planet and get closer to its center, your weight will decrease. Explain.

To determine

To explain: The weight variation if going towards center, using a hole to the center, or standing still on a shrinking planet.

Explanation of Solution

Introduction: Weight is the measurement of gravitational force applied on an object times the mass of the object.

If a person is standing on a shrinking planet, the center of mass will exert more force on the person as the planet shrinks. Thus, the greater force of gravity will be applied to the person as he reaches towards the center of the planet.

If he borrows a hole into the planet to get closer to the center of the planet, then the upward force exerted by the shell of the planet above him will counterbalance with the downward pull towards the center of the planet. The net force will be zero as he moves towards the center, acceleration due to gravity decreases. Thus, the weight of the person also decreases with the same rate.

Conclusion: Thus, if a person standing on the shrinking planet, then force exerted by center of mass will act upon it, increasing his weight. If going towards the center using a tunnel then downward force and upward force will balance each other and weigh lesser.