P.3.7.2.2 Gravitational field strength

The Earth can be assumed to be a uniform sphere of radius R. What is the mean density of the Earth?

• 
• 
• 
• 

The distance between the Sun and Mars varies from 2.1 × 10¹¹ m to 2.5 × 10¹¹ m. When Mars is closest to the Sun, the force of gravitational attraction between them is F. What is the force of gravitational attraction between them when they are furthest apart?

• 0.71F

• 0.84F

• 1.2F

• 1.4F

An electron on the surface of the Earth is placed in an electric field of strength 5000 N C⁻¹. What is (electrical force/gravitational force) for the electron?

• 1.1 × 10⁻¹⁴

• 2.9 × 10⁻¹⁰

• 3.4 × 10⁹

• 9.0 × 10¹³

A planet has a radius half the Earth’s radius and a mass a quarter of the Earth’s mass. What is the approximate gravitational field strength on the surface of the planet?

• 1.6 N kg^–1

• 5.0 N kg^–1

• 10 N kg–1

• 20 N kg^–1

Two stars of mass M and 4M are at a distance d between their centres.

The resultant gravitational field strength is zero along the line between their centres at a distance y from the centre of the star of mass M.

What is the value of the ratio y/d ?

• 1/2

• 1/3

• 2/3

• 3/4

Two identical uniform spheres each of radius R are placed in contact. The gravitational force between them is F.

The spheres are now separated until the force of attraction is F/9.

What is the distance between the surfaces of the spheres after they have been separated?

• 2R

• 4R

• 8R

• 12R

A satellite of mass m is in a circular orbit at height R above the surface of a uniform spherical planet of radius R and density ρ. What is the force of gravitational attraction between the satellite and the planet?

• 
• 
• 
• 

The following data refers to two planets, P and Q.

The gravitational field strength at the surface of P is 13.4 N kg^–1.

What is the gravitational field strength at the surface of Q?

• 3.4 N kg^–1

• 13.4 N kg^–1

• 53.6 N kg^–1

• 80.4 N kg^–1

The diagram shows an isolated binary star system. The two stars have equal masses, M, and the distance between their centres is r. The point P is half-way between the two stars. What is the gravitational field strength at P?

• zero

• 
• 
• 

In the equation below, X represents a physical variable in an electric or a gravitational field, a is a constant, b is either mass or charge and n is a number.

 $X\ =\frac{ab}{r^n}$  
Which line, A to D, in the table provides a consistent representation of X, a and b according to the value of n?

The symbols E, g, V and r have their usual meanings.

• A

• B

• C

• D