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Gravitational potential at the surface of Mercury

Please refer to the attachment for complete and all the questions. I am looking for brief explanations along with the answer.

11. The gravitational potential at the surface of Earth is V. The radius of Mercury is about one third the radius of Earth. Earth and Mercury are spheres of the same density. What is the gravitational potential at the surface of Mercury?

27. In the two circuits X and Y below, each cell has an e.m.f. E and negligible internal resistance. Each resistor has a resistance R. The power dissipated in circuit X is P. Compute the best estimate for the power dissipated in circuit Y.

28. Which one of the following diagrams best represents equipotential surfaces due to a point charge? (The point charge is represented by the filled circle.)

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Solution Preview

Explanations are in the attached file.

Given the same density, the mass of a ball of radius r is proportional to r3, whereas given some mass the potential is proportional to 1/r.
Therefore, given the same density, the gravitational potential on the surface of a ball is proportional to r3/r = r2 and so A is the correct answer.

The resistance of a parallel ...

Solution Summary

The expert examines the gravitational potential at the surface of Mercury.