Lesson test: Gravitation

Sign in

Libre University uses your GitHub account. Signing in is only needed to sit a final test, so the score is kept on your profile.

Gravitation

1.[3p]
What does Kepler's third law, combined with the second law of motion, force the gravitational force to be?

Proportional to the inverse square of the distance

Correct

Proportional to the inverse of the distance

The answer is: Proportional to the inverse square of the distance

Constant with distance

The answer is: Proportional to the inverse square of the distance

Proportional to the inverse cube of the distance

The answer is: Proportional to the inverse square of the distance

2.[2p]
The Moon's centripetal acceleration is $2.72 \times 10^{- 3}$ m s⁻². By what factor is that smaller than $g = 9.81$ m s⁻² at the Earth's surface?

CorrectNot quite: 3606

3.[3p]
Venus has a mass of $4.867 \times 10^{24}$ kg and a radius of $6.052 \times 10^{6}$ m. What is its surface gravity, in m s⁻², with $G = 6.674 \times 10^{- 11}$ ?

CorrectNot quite: 8.87

4.[2p]
A uniform spherical shell exerts no net gravitational force on a body placed anywhere inside it.

True

Correct

False

The answer is: True

5.[3p]
Why is the mean density of the Earth, 5.51 times that of water, historically important?

It is about twice the density of surface rock, so the interior must be much denser than the crust

Correct

It shows the Earth is hollow

The answer is: It is about twice the density of surface rock, so the interior must be much denser than the crust

It fixes the value of $g$ at the surface

The answer is: It is about twice the density of surface rock, so the interior must be much denser than the crust

It proves the Earth is a perfect sphere

The answer is: It is about twice the density of surface rock, so the interior must be much denser than the crust

6.[3p]
What is the escape velocity from a body of mass $6.417 \times 10^{23}$ kg and radius $3.390 \times 10^{6}$ m, in metres per second?

CorrectNot quite: 5027

7.[3p]
Which of these are true of gravitational potential energy written as $U = - G M m / r$ ?

Select all that apply

The zero is taken at infinite separation

Correct

A bound system has negative total energy

Correct

Close to a planet's surface it reduces to $m g h$ for small height changes

Correct

It becomes positive when the two bodies are very close together

The answer is: The zero is taken at infinite separation, A bound system has negative total energy, Close to a planet's surface it reduces to $mgh$ for small height changes

8.[2p]
Inside a uniform planet of radius $R$ , gravity varies as $g (r) = G M r / R^{3}$ . At half the radius, what fraction of the surface value is it?

CorrectNot quite: 0.5

9.[3p]
Match each person to what they contributed to the theory of gravity.

Tycho Brahe
Johannes Kepler
Isaac Newton
Henry Cavendish

naked eye observations accurate to about two arcminutes
a torsion balance measurement giving the Earth's density
the universal inverse square law and the shell theorem
three empirical laws of planetary motion

Show the answer

Tycho Brahe: naked eye observations accurate to about two arcminutes Johannes Kepler: three empirical laws of planetary motion Isaac Newton: the universal inverse square law and the shell theorem Henry Cavendish: a torsion balance measurement giving the Earth's density

1.[3p] What does Kepler's third law, combined with the second law of motion, force the gravitational force to be?

2.[2p] The Moon's centripetal acceleration is 2.72×10-3 m s⁻². By what factor is that smaller than g=9.81 m s⁻² at the Earth's surface?

3.[3p] Venus has a mass of 4.867×1024 kg and a radius of 6.052×106 m. What is its surface gravity, in m s⁻², with G=6.674×10-11?

4.[2p] A uniform spherical shell exerts no net gravitational force on a body placed anywhere inside it.

5.[3p] Why is the mean density of the Earth, 5.51 times that of water, historically important?

6.[3p] What is the escape velocity from a body of mass 6.417×1023 kg and radius 3.390×106 m, in metres per second?

7.[3p] Which of these are true of gravitational potential energy written as U=-GMm/r?

8.[2p] Inside a uniform planet of radius R, gravity varies as g(r)=GMr/R3. At half the radius, what fraction of the surface value is it?

9.[3p] Match each person to what they contributed to the theory of gravity.

1.[3p]
What does Kepler's third law, combined with the second law of motion, force the gravitational force to be?

2.[2p]
The Moon's centripetal acceleration is $2.72 \times 10^{- 3}$ m s⁻². By what factor is that smaller than $g = 9.81$ m s⁻² at the Earth's surface?

3.[3p]
Venus has a mass of $4.867 \times 10^{24}$ kg and a radius of $6.052 \times 10^{6}$ m. What is its surface gravity, in m s⁻², with $G = 6.674 \times 10^{- 11}$ ?

4.[2p]
A uniform spherical shell exerts no net gravitational force on a body placed anywhere inside it.

5.[3p]
Why is the mean density of the Earth, 5.51 times that of water, historically important?

6.[3p]
What is the escape velocity from a body of mass $6.417 \times 10^{23}$ kg and radius $3.390 \times 10^{6}$ m, in metres per second?

7.[3p]
Which of these are true of gravitational potential energy written as $U = - G M m / r$ ?

8.[2p]
Inside a uniform planet of radius $R$ , gravity varies as $g (r) = G M r / R^{3}$ . At half the radius, what fraction of the surface value is it?

9.[3p]
Match each person to what they contributed to the theory of gravity.