Variation of Acceleration Due to Gravity

📚 Key Concepts

🔹 Real-Life Example: Why Your Weight Changes Across the Globe

A person weighing 70 kg in New Delhi would weigh about 69.8 kg in Mumbai (due to latitude) and 69.9 kg on Mount Everest (due to altitude). Even GPS satellites must account for these small variations, as they orbit at different altitudes and experience slightly different gravitational pulls.

🔹 Variation of g: The acceleration due to gravity (g) varies with altitude, depth, and latitude because of Earth’s rotation and its slightly flattened shape at the poles.

Variation in Acceleration due to Gravity

🧪 Important Formulas

🔸 How g Changes with Conditions

1. ⬆ With Altitude

g decreases as we go higher above Earth’s surface.
Formula: g′ = g(1 – 2h/R)
Where: h = height above surface, R = Earth’s radius

2. ⬇ With Depth

g decreases as we go deeper into Earth.
Formula: g′ = g(1 – d/R)
Where: d = depth below surface

3. 🌐 With Latitude

g is maximum at the poles (~9.83 m/s²)
g is minimum at the equator (~9.78 m/s²)
Due to Earth’s rotation and oblate shape

🔍 Advanced: Class 11 Level Formulae (For Curious Minds)

For small heights: g₁ = g(1 – 2h/R)
For small depths: g₂ = g(1 – d/R)

🔹 Key Concept: Role of Earth’s Shape & Rotation

Earth’s rotation creates a small outward centrifugal force that opposes gravity, strongest at the equator and zero at the poles. Along with the Earth’s slightly flattened shape, this makes gravity weakest at the equator and strongest at the poles.