Grade 11 Physical Sciences · Mechanics · Apply Newton's law of gravitation

Apply Newton's law of gravitation Grade 11

Calculate the pull between two masses with F = Gm₁m₂/d², or find g on another planet, and say how distance changes the force.

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Question 1.2 · May/June 2025 · Paper 1 · National (DBE) · 2 marks

Various options are provided as possible answers to the following questions. Each question has only ONE correct answer. Choose the answer and write only the letter (A–D) next to the question numbers (1.1 to 1.10) in the ANSWER BOOK, e.g. 1.11 E.

1.2 Two large objects P and R, each of mass m, are placed with their centres r metres apart, as shown in the diagram below. They exert a gravitational force of magnitude F on each other.

The mass of R is increased to 2m and the objects are now placed so that the distance between their centres is 2r metres.

Which ONE of the following is the magnitude of the gravitational force that R now exerts on P?(2) Diagram for question 1.2

A $\frac{1}{2}$ F
B F
C 2F
D 4F

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: apply newton's law of gravitation

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3. Question 1.4 · May/June 2022 · Paper 1 · National (DBE) · 2 marks
Various options are provided as possible answers to the following questions. Each question has only ONE correct answer. Choose the answer and write only the letter (A–D) next to the question numbers (1.1 to 1.10) in the ANSWER BOOK, e.g. 1.11 E.
1.4 Object X exerts a gravitational force $F$ on object Y when the distance between the centres of the objects is $r$ .

The distance $r$ is now DOUBLED.

Which ONE of the following represents the gravitational force that X now exerts on Y?(2)
1. A $\frac{1}{4} F$
2. B $\frac{1}{2} F$
3. C $2 F$
4. D $4 F$
Show the memo (2 ticks)Memo
1. ✓
  Choose the correct option $F = \frac{G m _{1} m _{2}}{r ^{2}}$ , so $F \propto \frac{1}{r ^{2}}$ . With $2 r$ : $F^{'} = \frac{G m _{1} m _{2}}{( 2 r ) ^{2}} = \frac{1}{4} F$ .
  
  Answer: A
  2 marks · Apply Newton's law of gravitation
4. Question 5.5 · November 2019 · Paper 1 · National (DBE) · 2 marks
The relationship between gravitational acceleration and the ratio of the mass to the square of the radius ( $\frac{M}{R ^{2}}$ ) of different planets are investigated.

The graph below is obtained from the data collected.
5.5 Calculate the mass of Uranus if the radius is $2, 54 \times 1 0^{7}$ m.(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitution $\frac{M}{R ^{2}} = 1, 35 \times 1 0^{11}$
  $\frac{M}{( 2 , 54 \times 1 0 ^{7} ) ^{2}} = 1, 35 \times 1 0^{11}$
  1 mark · Apply Newton's law of gravitation
2. ✓
  Answer with unit $M = 8, 71 \times 1 0^{25}$ kg
  1 mark · Apply Newton's law of gravitation
5. Question 6.2 · November 2018 · Paper 1 · National (DBE) · 4 marks
The gravitational force on a probe, called Curiosity, on the surface of Mars is $3338$ N. The radius of Mars is $3390$ km and the mass of the planet is $6, 39 \times 1 0^{23}$ kg.
6.2 Calculate the mass of the probe.(4)
Show the memo (4 ticks)Memo
1. ✓
  Formula $F = \frac{G m _{1} m _{2}}{r ^{2}}$
  1 mark · Apply Newton's law of gravitation
2. ✓
  Force substituted $3338 = \dots$
  1 mark · Apply Newton's law of gravitation
3. ✓
  Substitution $3338 = \frac{( 6 , 67 \times 1 0 ^{- 11} ) ( 6 , 39 \times 1 0 ^{23} ) m}{( 3 390 \times 1 0 ^{3} ) ^{2}}$
  1 mark · Apply Newton's law of gravitation
4. ✓
  Answer with unit $m = 900$ kg
  1 mark · Apply Newton's law of gravitation
6. Question 1.2 · September 2026 · Paper 1 · Provincial · 2 marks
Four options are provided as possible answers to the following questions. Choose the answer and write only the letter (A–D) next to the question numbers (1.1 to 1.10) in the ANSWER BOOK.
1.2 The acceleration due to gravity on Earth is $g$ .

Which ONE of the following represents the acceleration due to gravity on a planet that has TWICE the mass and HALF the radius of the Earth?(2)
1. A $8 g$
2. B $4 g$
3. C $2 g$
4. D $\frac{1}{2} g$
Show the memo (2 ticks)Memo
1. ✓
  Correct option $g = \frac{GM}{r ^{2}}$
  
  $g_{pl an e t} = \frac{G ( 2 M )}{( \frac{1}{2} r ) ^{2}} = \frac{2 GM}{\frac{1}{4} r ^{2}} = 8 \frac{GM}{r ^{2}} = 8 g$
  
  Answer: A
  2 marks · Apply Newton's law of gravitation

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