Gravitation Solved Examples (Class 9 Physics)
Gravitation is the force of attraction between all objects with mass. Newton's law of universal gravitation explains planetary motion and helps us understa
TL;DR: Gravitation is the force of attraction between all objects with mass. Newton's law of universal gravitation explains planetary motion and helps us und…
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Gravitation is the force of attraction between all objects with mass. Newton's law of universal gravitation explains planetary motion and helps us understa
Gravitation — Solved Numerical Examples (Step by Step)
Example 1: Calculate the gravitational force between two objects of masses 2 kg and 3 kg separated by a distance of 2 m. (G = 6.67 × 10^-11 N·m^2/kg^2)
Solution: Given:
Mass m1 = 2 kg
Mass m2 = 3 kg
Distance r = 2 m
Gravitational constant G = 6.67 × 10^-11 N·m^2/kg^2
Using Newton's law of universal gravitation:
F = G × (m1 × m2) / r^2
F = 6.67 × 10^-11 × (2 × 3) / (2)^2
F = 6.67 × 10^-11 × 6 / 4
F = 6.67 × 10^-11 × 1.5
F = 10 × 10^-11 N = 10^-10 N
Example 2: The mass of Earth is 6 × 10^24 kg and its radius is 6.4 × 10^6 m. Calculate the acceleration due to gravity at Earth's surface. (G = 6.67 × 10^-11 N·m^2/kg^2)
Solution: Given:
Mass of Earth M = 6 × 10^24 kg
Radius of Earth R = 6.4 × 10^6 m
G = 6.67 × 10^-11 N·m^2/kg^2
Using the formula: g = GM / R^2
g = (6.67 × 10^-11) × (6 × 10^24) / (6.4 × 10^6)^2
g = (6.67 × 6) / (6.4)^2 × 10^(-11+24-12)
g = 40.02 / 40.96 × 10^1
g ≈ 9.8 m/s^2
Example 3: Find the weight of a 70 kg person on Earth where g = 10 m/s^2.
Solution: Given:
Mass m = 70 kg
Acceleration due to gravity g = 10 m/s^2
Using the formula: Weight W = mg
W = 70 × 10
W = 700 N
Example 4: If the distance between two masses is doubled, how does the gravitational force change?
Solution: Using Newton's law of universal gravitation: F = G × (m1 × m2) / r^2
If distance r is doubled to 2r:
F' = G × (m1 × m2) / (2r)^2
F' = G × (m1 × m2) / 4r^2
F' = F / 4
So the force becomes 1/4 of the original force.
Example 5: Calculate the orbital velocity of an object orbiting Earth at a height equal to Earth's radius above the surface. (g = 10 m/s^2, R = 6.4 × 10^6 m)
Solution: Given:
Height h = R (equal to Earth's radius)
Radius of orbit r = R + h = 2R
g = 10 m/s^2
R = 6.4 × 10^6 m
At the orbital height, acceleration g' = g / 4 = 2.5 m/s^2 (since g is inversely proportional to r^2)
For circular orbit: v = sqrt(g' × r)
v = sqrt(2.5 × 2 × 6.4 × 10^6)
v = sqrt(32 × 10^6)
v ≈ 5.66 × 10^3 m/s = 5.66 km/s
Example 6: The weight of a person on the Moon is 1/6 of their weight on Earth. If a person weighs 600 N on Earth, what is their weight on the Moon?
Solution: Given:
Weight on Earth = 600 N
Weight on Moon = (1/6) × Weight on Earth
Weight on Moon = (1/6) × 600
Weight on Moon = 100 N
Example 7: A satellite has a period of 24 hours and orbits Earth. What can you deduce about this satellite?
Solution: Given:
Period of orbit T = 24 hours
Earth's rotation period = 24 hours
Since the satellite's orbital period equals Earth's rotation period, the satellite appears stationary relative to a point on Earth's surface. This is a geostationary satellite. It remains above the same location on the equator.
Tips
- Newton's law of universal gravitation F = G(m1m2)/r^2 shows that force is inversely proportional to distance squared. Doubling distance makes force 1/4, tripling distance makes it 1/9.
- Weight changes with location but mass does not. The acceleration due to gravity g varies with location. On Moon, g is 1/6 of Earth's g, so weight on Moon is 1/6 of weight on Earth.
- For circular orbits, the centripetal force equals the gravitational force. This relationship is used to find orbital velocity and period.
Frequently Asked Questions
Why do planets orbit the Sun and not fall into it?
Planets orbit the Sun because they have velocity perpendicular to the gravitational force. The gravitational force acts as the centripetal force, pulling the planet toward the Sun, but the planet's velocity keeps it moving in a circular or elliptical orbit rather than falling straight in.
What is the difference between g and G?
G is the universal gravitational constant (6.67 × 10^-11 N·m^2/kg^2) and is the same everywhere. g is the acceleration due to gravity at a specific location and varies. On Earth's surface, g ≈ 10 m/s^2. They are related by g = GM/R^2.
More Physics Solved Examples
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- Force and Laws of Motion
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