Gravitation – Board Exam Numericals
Stage 2 • Page 3 • Solved Numerical Problems
Numerical 1: Calculate the gravitational force between two masses of 5 kg and 10 kg separated by 2 m.
Given:
- m1 = 5 kg
- m2 = 10 kg
- r = 2 m
- G = 6.67 × 10−11 N m² kg−2
Formula:
F = G (m1 m2) / r²
Substitution:
F = 6.67 × 10−11 × (5 × 10) / 2²
Calculation:
F = 8.34 × 10−10 N
Answer: Gravitational force = 8.34 × 10−10 N
Numerical 2: Find the weight of a body of mass 60 kg on Earth.
Given:
- m = 60 kg
- g = 9.8 m/s²
Formula:
W = mg
Substitution:
W = 60 × 9.8
Answer:
W = 588 N
Numerical 3: Calculate acceleration due to gravity on a planet whose mass is twice that of Earth and radius is twice Earth’s radius.
Using:
g = GM / R²
For the planet:
- M′ = 2M
- R′ = 2R
g′ = G(2M)/(2R)² = 2GM / 4R²
g′ = g / 2
Answer: Acceleration due to gravity becomes half of Earth’s value.
Numerical 4: Calculate escape velocity from Earth (Given g = 9.8 m/s², R = 6.4 × 106 m).
Formula:
ve = √(2gR)
Substitution:
ve = √(2 × 9.8 × 6.4 × 106)
Answer:
ve ≈ 11.2 km/s
Numerical 5: A body weighs 490 N on Earth. What is its mass?
Given:
- W = 490 N
- g = 9.8 m/s²
Formula:
m = W / g
Calculation:
m = 490 / 9.8 = 50 kg
Board Exam Tips for Numericals
- Write Given → Formula → Substitution → Answer
- Always include units
- Box final answers
- Avoid skipping steps
- Use g = 9.8 unless stated otherwise
Stage 2 • Page 3 Completed Successfully ✅
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- Gravitation – Part 9
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