These questions revise the lessons in gravitation. Use G = 6.67 × 10⁻¹¹ N m² kg⁻², GM for Earth = 3.98 × 10¹⁴ N m² kg⁻¹, and g = 9.81 N kg⁻¹ on Earth’s surface.
Work each question on paper before opening the answer.
Questions
Question 1
Find the weight of an 8.0 kg parcel on Earth.
Answer
W = mg = 8.0 × 9.81 = 78.5 N. The unit is the newton, because weight is a force.
Question 2
An astronaut has a mass of 70 kg. On the Moon, g = 1.62 N kg⁻¹. State the astronaut’s mass and weight there.
Answer
The mass is still 70 kg. The weight is 70 × 1.62 = 113 N.
Question 3
Two masses of 5.0 kg and 20 kg are 0.50 m apart. Find the gravitational force between them.
Answer
F = Gm₁m₂ ÷ r² = 6.67 × 10⁻¹¹ × 5.0 × 20 ÷ 0.25 = 2.67 × 10⁻⁸ N. The force is tiny, which is why we do not notice it between everyday objects.
Question 4
The distance between two masses is doubled. What happens to the gravitational force between them?
Answer
F ∝ 1 ÷ r², so doubling r divides the force by 2² = 4. The force becomes one quarter of its original value.
Question 5
Find the gravitational field strength at a height where the distance from Earth’s centre is twice Earth’s radius.
Answer
g ∝ 1 ÷ r², so g = 9.81 ÷ 4 = 2.45 N kg⁻¹.
Question 6
A satellite orbits at a radius of 7.0 × 10⁶ m. Find its orbital speed.
Answer
v = √(GM ÷ r) = √(3.98 × 10¹⁴ ÷ 7.0 × 10⁶) = √(5.69 × 10⁷) = 7.54 × 10³ m s⁻¹.
Question 7
Planet P orbits a star with a period of 1.0 year. Planet Q orbits the same star at four times the radius. Find Q’s period.
Answer
T² ∝ r³, so T_Q² = 1.0² × 4³ = 64. Then T_Q = 8.0 years.
Question 8
Explain why astronauts in orbit float although gravity still acts on them.
Answer
Gravity provides the centripetal force that keeps the spacecraft and the astronauts in orbit. They are in free fall together, so no surface pushes back on them, and they appear weightless.
If you got these wrong
- Questions 1 and 2: revise mass, weight and gravitational field strength.
- Questions 3 to 5: revise applying Newton’s law of gravitation.
- Questions 6 and 8: revise centripetal force in orbital motion.
- Question 7: revise orbital relationships with consistent units.
Log the failing step in the mistake log and paper error review, or set a timed round with the timed original practice session builder. To practise with a teacher, see online one-to-one Physics tuition.