Gravitation – Board Exam Questions & Answers

Stage 2 • Page 2 • Long Answer Questions

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Q1. Derive the expression for acceleration due to gravity on the surface of Earth.

According to Newton’s law of gravitation, the gravitational force between Earth and a body of mass m on its surface is:

F = G (Mm / R²)

This force produces acceleration g in the body:

F = mg

Equating the two expressions:

mg = G (Mm / R²)

Cancelling m on both sides:

g = GM / R²

Thus, acceleration due to gravity depends on the mass and radius of Earth.

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Q2. Derive the expression for variation of g with height above Earth’s surface.

At a height h above Earth’s surface, distance from Earth’s centre is (R + h).

Acceleration due to gravity at height h:

g_h = GM / (R + h)²

Dividing by g = GM / R²:

g_h / g = (R / (R + h))²

For small heights (h ≪ R):

g_h ≈ g (1 − 2h/R)

Hence, acceleration due to gravity decreases with increase in height.

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Q3. Explain variation of acceleration due to gravity with depth.

At a depth d below Earth’s surface, distance from Earth’s centre is (R − d).

Acceleration due to gravity at depth d is:

g_d = g (1 − d/R)

• g decreases linearly with depth
• g becomes zero at Earth’s centre

This happens because gravitational pull from all directions cancels at the centre.

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Q4. Distinguish between mass and weight.

Mass	Weight
Quantity of matter	Gravitational force
Constant	Variable
Scalar	Vector
kg	N

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Q5. Derive the expression for escape velocity of a body from Earth.

Escape velocity is the minimum velocity required to take a body from Earth’s surface to infinity with zero velocity.

Initial energy = Final energy

At Earth’s surface:

Total Energy = ½ m v_e² − GMm / R

At infinity:

Total Energy = 0

Equating:

½ m v_e² = GMm / R

Thus:

v_e = √(2GM / R) = √(2gR)

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Exam Writing Tips

• Always start derivations from basic laws
• Write formulas clearly and boxed if possible
• Mention assumptions (h ≪ R, no air resistance)
• Use correct units and symbols

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Stage 2 • Page 2 Completed Successfully ✅

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• Gravitation – Part 1
• Gravitation – Part 2
• Gravitation – Part 3
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• Gravitation – Part 7
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• Gravitation – Part 9
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• Gravitation – Part 14
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• Gravitation – Part 17
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• Gravitation – Part 19
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• Gravitation – Part 26
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