Gauss law or not?

Three point masses are distributed at corners of a triangle. Which approach is the best to calculate the gravitational potential/field due to these masses?

1. Gauss law
2. Good old Newton's law of gravitation
3. Green's function method

Ans: B or C (they are equivalent!)

Gauss law or not?

A thin straight wire with a uniform density exists. Which approach is the best way to calculate the gravitational potential/field due to it? We consider the wire very long -- infinite in length in fact.

1. Gauss law
2. Good old Newton's law of gravitation

Ans: A

Travelling through the center of the earth

A straight hole is drilled through the center of the earth and a person (with the Iron Man suit) drops into that hole. It is known that that person will appear on the opposite side of the earth in mere 42 minutes. What is the nature of the motion that this person goes through? (Ignore the earth spin and air friction. Assume that the density is uniform.)

1. Const. acceleration and then const. deceleration
2. Simple harmonic motion
3. A complicated motion that is none of the above

Ans: B (calculate and prove it yourself!)

A fun ride

A straight hole is drilled through the earth, but the drilled path does not go through the center of the earth. A person (with the Iron Man suit) drops into that hole. What is the nature of the motion that this person goes through? (Ignore the earth spin and air friction. Assume that the density is uniform.)

1. Const. acceleration and then const. deceleration
2. Simple harmonic motion
3. A complicated motion that is none of the above

Ans: B (calculate and prove it yourself!)

A fun ride

A straight hole is drilled through the earth, but the drilled path does not go through the center of the earth. A person (with the Iron Man suit) drops into that hole. How long does it take for the person to appear on the other side of the hole? (Ignore the earth spin and air friction. Assume that the density is uniform.)

1. 42 minutes (same as going through the center)
2. 21 minutes
3. Depends on the length of the drilled path

Ans: A (calculate and prove it yourself! -- and post your solution on the forum)