Universal law of gravitation: Class 9 practice
F = Gm₁m₂/r² with G = 6.67 × 10⁻¹¹ N m² kg⁻². Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Scientific notation
The idea behind universal law of gravitation
F = Gm₁m₂/r² with G = 6.67 × 10⁻¹¹ N m² kg⁻². Force halves when one mass halves and becomes one quarter when the distance doubles.
Step-by-step method
- Write masses in kg and r in m.
- Substitute into F = Gm₁m₂/r².
- For ratio questions, use F ∝ m₁m₂/r².
Worked example 1 (Basic)
Find the gravitational force between 73 kg and 38 kg placed 5 m apart.
- F = 6.67 × 10⁻¹¹ × 73 × 38 / 25
- = 7.401e-9 N
- Answer: 7.401e-9 N
Worked example 2 (Standard)
Find the gravitational force between 75 kg and 55 kg placed 5 m apart.
- F = 6.67 × 10⁻¹¹ × 75 × 55 / 25
- = 1.101e-8 N
- Answer: 1.101e-8 N
Worked example 3 (Challenge)
If one mass is multiplied by 2 and the distance by 2, what happens to the force?
- F ∝ m/r²
- New F = 2/4 of old
- Answer: Becomes 1/2 times
Common mistakes and misconceptions
- Not squaring r
- Using cm instead of m
Practice questions
- (Basic) Find the gravitational force between 22 kg and 90 kg placed 2 m apart.
- (Basic) Find the gravitational force between 80 kg and 40 kg placed 3 m apart.
- (Standard) Find the gravitational force between 83 kg and 23 kg placed 2 m apart.
- (Standard) Find the gravitational force between 45 kg and 52 kg placed 1 m apart.
- (Challenge) If one mass is multiplied by 3 and the distance by 2, what happens to the force?
- (Challenge) If one mass is multiplied by 3 and the distance by 3, what happens to the force?
Answer key with full working
- Q1: F = 6.67 × 10⁻¹¹ × 22 × 90 / 4 → = 3.302e-8 N → Answer: 3.302e-8 N
- Q2: F = 6.67 × 10⁻¹¹ × 80 × 40 / 9 → = 2.372e-8 N → Answer: 2.372e-8 N
- Q3: F = 6.67 × 10⁻¹¹ × 83 × 23 / 4 → = 3.183e-8 N → Answer: 3.183e-8 N
- Q4: F = 6.67 × 10⁻¹¹ × 45 × 52 / 1 → = 1.561e-7 N → Answer: 1.561e-7 N
- Q5: F ∝ m/r² → New F = 3/4 of old → Answer: Becomes 3/4 times
- Q6: F ∝ m/r² → New F = 3/9 of old → Answer: Becomes 1/3 times
Syllabus note
This skill is listed under "Gravitation" for Class 9 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is universal law of gravitation in?
"Gravitation", Class 9 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.