Gravitation – Complete Intermediate Notes

Stage 1 • Page 3 • Variation of Acceleration due to Gravity (g)

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1. Why Does g Vary?

Although g ≈ 9.8 m s⁻² near Earth’s surface, it is not constant. It varies due to:

• Change in distance from Earth’s centre
• Rotation of Earth
• Shape of Earth

Exam Insight:
Most numerical problems are based on variation of g, not its average value.

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2. Variation of g with Height (Above Earth’s Surface)

At a height h above Earth’s surface, the distance from Earth’s centre becomes:

r = R + h

Acceleration due to gravity at height h:

g_h = g ( R / (R + h) )²

For small heights (h ≪ R), we use approximation:

g_h ≈ g (1 − 2h/R)

• g decreases as height increases
• g → 0 as h → ∞

IIT Tip:
Use approximation only when h ≪ R, otherwise use full formula.

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3. Variation of g with Depth (Below Earth’s Surface)

At a depth d below Earth’s surface, distance from centre is:

r = R − d

Acceleration due to gravity at depth d:

g_d = g (1 − d/R)

• g decreases linearly with depth
• g = 0 at Earth’s centre

Board Exam Favourite:
Why g becomes zero at Earth’s centre → symmetric pull cancels.

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4. Graphical Representation of g

• g vs Height: Curve (inverse square nature)
• g vs Depth: Straight line decreasing to zero

IIT Angle:
Graph-based questions are frequently asked in JEE Main & Advanced.

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5. Comparison: g at Height vs g at Depth

At Height	At Depth
Inverse square relation	Linear relation
Never exactly zero	Zero at centre

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6. Common Errors Students Make

• Using height formula for depth problems
• Wrong approximation conditions
• Forgetting Earth’s radius
• Sign mistakes in formulas

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