P.3.7.2.3 Gravitational Potential

The graph shows how the gravitational potential varies with distance between two planets, K and L, that have the same radius.

Which statement is correct?

• The mass of L is greater than the mass of K.

• The gravitational field strength at the surface of L is greater than that at the surface of K.

• The escape velocity from planet L is greater than that from planet K.

• More work must be done to move a mass of 1 kg from the surface of K to a distant point, than 1 kg from the surface of L.

The diagram shows equipotential lines near a group of asteroids. Which arrow shows the direction of the gravitational field at X?

• ↑

• ↓

• ←

• →

Planet N has a gravitational potential –V at its surface. Planet M has double the density and double the radius of planet N. Both planets are spherical and have uniform density.

What is the gravitational potential at the surface of planet M?

• –16V

• –8V

• –4V

• –0.2V

The radius of a planet is R. The gravitational potential at the surface of the planet due to its mass is −4000 J kg⁻¹.

What is the gravitational potential at a distance 2R from the centre of the planet?

• −1000 J kg⁻¹

• −2000 J kg⁻¹

• −4000 J kg⁻¹

• −8000 J kg⁻¹

X and Y are two stars of equal mass M. The distance between their centres is d.

What is the gravitational potential at the mid-point P between them?

• 
• 
• 
• 

Which one of the following statements about gravitational potential is incorrect?

• It is analogous to the electric potential at a point in an electric field.

• It is equal to the gravitational potential energy of a mass of 1 kg.

• It is a vector quantity.

• The difference in gravitational potential between two points at different heights above the Earth depends on the position of the points.

Which one of the following statements about gravitational potential is correct?

• gravitational potential can have a positive value

• the gravitational potential at the surface of the Earth is zero

• the gravitational potential gradient at a point has the same numerical value as the gravitational field strength at that point

• the unit of gravitational potential is N kg^–1

A uniform electric field of electric field strength E is aligned so it is vertical. An ion moves vertically through a small distance Δd from point X to point Y in the field.There is a uniform gravitational field of field strength g throughout the region.

Which line, A to D, in the table correctly gives the gravitational potential difference, and the electric potential difference, between X and Y?

• A

• B

• C

• D

Mars has a diameter approximately 0.5 that of the Earth, and a mass of 0.1 that of the Earth.

The gravitational potential at the Earth’s surface is −63 MJ kg^–1.

What is the approximate value of the gravitational potential at the surface of Mars?

• −13 MJ kg^–1

• −25 MJ kg^–1

• −95 MJ kg^–1

• −320 MJ kg^–1

The diagram shows two points, P and Q, at distances r and 2r from the centre of a planet. The gravitational potential at P is −16 kJ kg⁻¹. What is the work done on a 10 kg mass when it is taken from P to Q?

• – 120 kJ

• – 80 kJ

• + 80 kJ

• + 120 kJ