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gravitation formulas pyqs Sheet

Complete Class 11 gravitation formulae, NCERT examples, CBSE/NEET/JEE/IB/IGCSE/A-Level questions, quick revision notes and clean exam-focused diagrams.

Formula SheetNCERTCBSENEETJEE MainJEE AdvancedIBIGCSEA-Level

Complete Formula Sheet

Use SI units unless stated otherwise. In all satellite formulae, r means distance from the centre of the planet, not height above the surface.

Most Used

F = Gm₁m₂/r²

g = GM/R²

V = -GM/r

Satellite

v = √(GM/r)

T = 2π√(r³/GM)

E = -GMm/2r

Escape and Kepler

v_e = √(2GM/R)

v_e = √2 v_o

T² proportional to r³

Gravitation Formulae

Universal Gravitation Formulae

Concept	Formula	Meaning	Exam Tip
Universal law	F = Gm₁m₂/r²	Attractive force between two point masses.	Use centre-to-centre separation.
Vector force on m₁	F₁₂ = -Gm₁m₂r/r³	Negative sign shows attraction.	Define direction of r clearly.
Superposition	F_net = F₁ + F₂ + ...	Net force is vector sum.	Resolve components in 2D problems.
G units	G = 6.67 x 10^-11 N m² kg^-2	Universal gravitational constant.	Dimensions: [M^-1L³T^-2].

Force Between Two Masses

g Formulae

Acceleration Due to Gravity Formulae

Concept	Formula	Meaning	Exam Tip
Surface gravity	g = GM/R²	Acceleration due to gravity at surface.	M and R are planet mass and radius.
Height h	g_h = g(R/(R+h))²	Gravity decreases with height.	For h << R: g_h = g(1 - 2h/R).
Depth d	g_d = g(1 - d/R)	Inside uniform Earth approximation.	At centre, d = R, so g = 0.
Latitude	g_λ = g - ω²R cos²λ	Effective g due to rotation.	Minimum at equator, maximum at poles.
Rotation at equator	g' = g - ω²R	Centrifugal effect reduces measured g.	Use only for effective gravity.
Relation with density	g = 4πGρR/3	For uniform sphere.	Useful for density-based MCQs.

Variation of g

Gravitational Field Formulae

Field Formulae

Concept	Formula	Meaning	Exam Tip
Field intensity	E = F/m	Force per unit test mass.	Direction is toward source mass.
Point mass field	E = GM/r²	Magnitude at distance r.	Same unit as g: N kg^-1.
Vector field	E = -GMr/r³	Radially inward field.	Negative sign shows attraction.
Solid sphere inside	E = GMr/R³	For r < R, uniform sphere.	Straight-line graph inside.
Solid sphere outside	E = GM/r²	For r >= R.	Inverse-square curve outside.
Thin shell inside	E = 0	Inside uniform spherical shell.	Important shell theorem result.

Field Graph

Potential Formulae

Gravitational Potential and Potential Energy

Concept	Formula	Meaning	Exam Tip
Potential	V = -GM/r	Potential due to point mass M.	Zero is taken at infinity.
Potential energy	U = -GMm/r	Energy of two masses.	Negative for bound system.
Field-potential relation	E = -dV/dr	Field is negative potential gradient.	Graph slope gives field.
Work done by external agent	W = ΔU = U_f - U_i	Slow movement without KE change.	Check sign carefully.
Work by gravity	W_g = -ΔU	Gravity does positive work when masses approach.	Conservative field.
Potential of shell inside	V = -GM/R	Constant inside a shell.	Field inside shell is zero.

Potential Graph

Satellite Formulae

Satellite Motion Formulae

Concept	Formula	Meaning	Exam Tip
Orbital speed	v_o = √(GM/r)	Circular orbit speed.	r is orbit radius from centre.
Time period	T = 2π√(r³/GM)	Period of circular satellite.	T² proportional to r³.
Angular velocity	ω = √(GM/r³)	Angular speed in circular orbit.	Also ω = 2π/T.
Kinetic energy	K = GMm/2r	Positive orbital kinetic energy.	Half magnitude of potential energy.
Potential energy	U = -GMm/r	Negative for bound satellite.	Zero at infinity.
Total energy	E = -GMm/2r	Bound circular orbit.	Binding energy = GMm/2r.
Orbit radius	r = R + h	Satellite height h above surface.	Never use h alone in orbital formula.
Geostationary	T = 24 h	Appears fixed above equator.	Approx height 35,786 km.

Animated Satellite Orbit

Escape Velocity Formulae

Concept	Formula	Meaning	Exam Tip
Surface escape speed	v_e = √(2GM/R)	Minimum speed to reach infinity.	Independent of projectile mass.
Using g	v_e = √(2gR)	Near spherical planet surface.	Use g = GM/R².
From height h	v_e = √(2GM/(R+h))	Escape from height h.	Distance from centre is R+h.
Relation with orbital speed	v_e = √2 v_o	At same radius.	Very common ratio result.
Energy condition	1/2 mv_e² = GMm/R	Minimum KE equals binding from surface.	Final total energy is zero.

Escape Velocity Concept

Kepler's Laws Summary

Kepler Formulae and Exam Notes

Concept	Formula	Meaning	Exam Tip
First law	Planets move in ellipses with Sun at one focus.	Orbit shape.	Sun is not generally at centre.
Second law	dA/dt = constant	Equal areas in equal time.	Planet is faster near perihelion.
Third law	T² proportional to r³	For circular orbit around same mass.	For ellipse use semi-major axis a.
Third law formula	T² = 4π²r³/GM	Circular orbit period.	Can find central mass M.
Ellipse formula	T² = 4π²a³/GM	Elliptical orbit.	Use semi-major axis, not instantaneous radius.

Second Law Area Diagram

NCERT Examples and Exercises

NCERT Example 1

Question: Find force between masses 2 kg and 3 kg separated by 1 m.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: F = 6.67 x 10^-11 x 2 x 3 / 1² = 4.00 x 10^-10 N.

Final Answer: 4.00 x 10^-10 N

NCERT Exercise 2

Question: At what height does g become nearly g/4?

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: 1/4 = (R/(R+h))²; R+h = 2R, so h = R.

Final Answer: h = R

CBSE PYQ 3

Question: Show that escape velocity is independent of mass of projectile.

Show Solution

Formula/Concept: 1/2 mv_e² = GMm/R

Solution: Mass m cancels from both sides. v_e = √(2GM/R).

Final Answer: Independent of projectile mass

NEET PYQ-style 4

Question: If radius of orbit is 4 times, time period becomes?

Show Solution

Formula/Concept: T proportional to r^3/2

Solution: T₂/T₁ = 4^3/2 = 8.

Final Answer: 8 times

JEE Main PYQ-style 5

Question: A satellite has total energy E. What is its binding energy?

Show Solution

Formula/Concept: Binding energy = -E for bound circular orbit

Solution: Since E is negative, binding energy is positive magnitude.

Final Answer: -E

JEE Advanced 6

Question: At perihelion and aphelion, distances are r_p and r_a. Find speed ratio.

Show Solution

Formula/Concept: Angular momentum conservation

Solution: mr_pv_p = mr_av_a; v_p/v_a = r_a/r_p.

Final Answer: r_a/r_p

IB Question 7

Question: Explain why gravitational potential is negative.

Show Solution

Formula/Concept: V = -GM/r

Solution: Zero is chosen at infinity. Work is needed to take mass from bound point to infinity.

Final Answer: Bound gravitational potential is negative.

IGCSE Question 8

Question: State one use of a geostationary satellite.

Show Solution

Formula/Concept: T = 24 h

Solution: It appears fixed above one region, so it is useful for communication.

Final Answer: Communication / broadcasting

A-Level Question 9

Question: Derive T² = 4π²r³/GM.

Show Solution

Formula/Concept: GMm/r² = mv²/r

Solution: v = 2πr/T. Substitute and rearrange.

Final Answer: T² = 4π²r³/GM

CBSE PYQs

CBSE PYQ 1

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

CBSE PYQ 2

Question: Find variation of g at height h.

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

CBSE PYQ 3

Question: Find orbital speed of satellite.

Show Solution

Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

CBSE PYQ 4

Question: Find escape speed from a planet.

Show Solution

Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

CBSE PYQ 5

Question: Use Kepler's third law for period ratio.

Show Solution

Formula/Concept: T² proportional to r³

Solution: T ratio equals radius ratio to the power 3/2.

Final Answer: Same central mass.

CBSE PYQ 6

Question: Find field inside solid sphere.

Show Solution

Formula/Concept: E = GMr/R³

Solution: Inside uniform sphere, field varies linearly with r.

Final Answer: At centre field is zero.

CBSE PYQ 7

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

CBSE PYQ 8

Question: Find variation of g at height h.

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

CBSE PYQ 9

Question: Find orbital speed of satellite.

Show Solution

Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

CBSE PYQ 10

Question: Find escape speed from a planet.

Show Solution

Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

CBSE PYQ 11

Question: Use Kepler's third law for period ratio.

Show Solution

Formula/Concept: T² proportional to r³

Solution: T ratio equals radius ratio to the power 3/2.

Final Answer: Same central mass.

CBSE PYQ 12

Question: Find field inside solid sphere.

Show Solution

Formula/Concept: E = GMr/R³

Solution: Inside uniform sphere, field varies linearly with r.

Final Answer: At centre field is zero.

NEET PYQs

NEET PYQ 1

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

NEET PYQ 2

Question: Find variation of g at height h.

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

NEET PYQ 3

Question: Find orbital speed of satellite.

Show Solution

Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

NEET PYQ 4

Question: Find escape speed from a planet.

Show Solution

Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

NEET PYQ 5

Question: Use Kepler's third law for period ratio.

Show Solution

Formula/Concept: T² proportional to r³

Solution: T ratio equals radius ratio to the power 3/2.

Final Answer: Same central mass.

NEET PYQ 6

Question: Find field inside solid sphere.

Show Solution

Formula/Concept: E = GMr/R³

Solution: Inside uniform sphere, field varies linearly with r.

Final Answer: At centre field is zero.

NEET PYQ 7

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

NEET PYQ 8

Question: Find variation of g at height h.

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

NEET PYQ 9

Question: Find orbital speed of satellite.

Show Solution

Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

NEET PYQ 10

Question: Find escape speed from a planet.

Show Solution

Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

NEET PYQ 11

Question: Use Kepler's third law for period ratio.

Show Solution

Formula/Concept: T² proportional to r³

Solution: T ratio equals radius ratio to the power 3/2.

Final Answer: Same central mass.

NEET PYQ 12

Question: Find field inside solid sphere.

Show Solution

Formula/Concept: E = GMr/R³

Solution: Inside uniform sphere, field varies linearly with r.

Final Answer: At centre field is zero.

NEET PYQ 13

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

NEET PYQ 14

Question: Find variation of g at height h.

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

NEET PYQ 15

Question: Find orbital speed of satellite.

Show Solution

Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

NEET PYQ 16

Question: Find escape speed from a planet.

Show Solution

Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

NEET PYQ 17

Question: Use Kepler's third law for period ratio.

Show Solution

Formula/Concept: T² proportional to r³

Solution: T ratio equals radius ratio to the power 3/2.

Final Answer: Same central mass.

NEET PYQ 18

Question: Find field inside solid sphere.

Show Solution

Formula/Concept: E = GMr/R³

Solution: Inside uniform sphere, field varies linearly with r.

Final Answer: At centre field is zero.

JEE Main PYQs

JEE Main PYQ 1

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

JEE Main PYQ 2

Question: Find variation of g at height h.

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

JEE Main PYQ 3

Question: Find orbital speed of satellite.

Show Solution

Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

JEE Main PYQ 4

Question: Find escape speed from a planet.

Show Solution

Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

JEE Main PYQ 5

Question: Use Kepler's third law for period ratio.

Show Solution

Formula/Concept: T² proportional to r³

Solution: T ratio equals radius ratio to the power 3/2.

Final Answer: Same central mass.

JEE Main PYQ 6

Question: Find field inside solid sphere.

Show Solution

Formula/Concept: E = GMr/R³

Solution: Inside uniform sphere, field varies linearly with r.

Final Answer: At centre field is zero.

JEE Main PYQ 7

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

JEE Main PYQ 8

Question: Find variation of g at height h.

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

JEE Main PYQ 9

Question: Find orbital speed of satellite.

Show Solution

Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

JEE Main PYQ 10

Question: Find escape speed from a planet.

Show Solution

Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

JEE Main PYQ 11

Question: Use Kepler's third law for period ratio.

Show Solution

Formula/Concept: T² proportional to r³

Solution: T ratio equals radius ratio to the power 3/2.

Final Answer: Same central mass.

JEE Main PYQ 12

Question: Find field inside solid sphere.

Show Solution

Formula/Concept: E = GMr/R³

Solution: Inside uniform sphere, field varies linearly with r.

Final Answer: At centre field is zero.

JEE Main PYQ 13

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

JEE Main PYQ 14

Question: Find variation of g at height h.

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

JEE Main PYQ 15

Question: Find orbital speed of satellite.

Show Solution

Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

JEE Main PYQ 16

Question: Find escape speed from a planet.

Show Solution

Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

JEE Main PYQ 17

Question: Use Kepler's third law for period ratio.

Show Solution

Formula/Concept: T² proportional to r³

Solution: T ratio equals radius ratio to the power 3/2.

Final Answer: Same central mass.

JEE Main PYQ 18

Question: Find field inside solid sphere.

Show Solution

Formula/Concept: E = GMr/R³

Solution: Inside uniform sphere, field varies linearly with r.

Final Answer: At centre field is zero.

JEE Advanced PYQs

JEE Advanced PYQ 1

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

JEE Advanced PYQ 2

Question: Find variation of g at height h.

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

JEE Advanced PYQ 3

Question: Find orbital speed of satellite.

Show Solution

Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

JEE Advanced PYQ 4

Question: Find escape speed from a planet.

Show Solution

Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

JEE Advanced PYQ 5

Question: Use Kepler's third law for period ratio.

Show Solution

Formula/Concept: T² proportional to r³

Solution: T ratio equals radius ratio to the power 3/2.

Final Answer: Same central mass.

JEE Advanced PYQ 6

Question: Find field inside solid sphere.

Show Solution

Formula/Concept: E = GMr/R³

Solution: Inside uniform sphere, field varies linearly with r.

Final Answer: At centre field is zero.

JEE Advanced PYQ 7

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

JEE Advanced PYQ 8

Question: Find variation of g at height h.

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

JEE Advanced PYQ 9

Question: Find orbital speed of satellite.

Show Solution

Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

JEE Advanced PYQ 10

Question: Find escape speed from a planet.

Show Solution

Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

JEE Advanced PYQ 11

Question: Use Kepler's third law for period ratio.

Show Solution

Formula/Concept: T² proportional to r³

Solution: T ratio equals radius ratio to the power 3/2.

Final Answer: Same central mass.

JEE Advanced PYQ 12

Question: Find field inside solid sphere.

Show Solution

Formula/Concept: E = GMr/R³

Solution: Inside uniform sphere, field varies linearly with r.

Final Answer: At centre field is zero.

IB Questions

IB Question 1

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

IB Question 2

Question: Find variation of g at height h.

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

IB Question 3

Question: Find orbital speed of satellite.

Show Solution

Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

IB Question 4

Question: Find escape speed from a planet.

Show Solution

Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

IB Question 5

Question: Use Kepler's third law for period ratio.

Show Solution

Formula/Concept: T² proportional to r³

Solution: T ratio equals radius ratio to the power 3/2.

Final Answer: Same central mass.

IB Question 6

Question: Find field inside solid sphere.

Show Solution

Formula/Concept: E = GMr/R³

Solution: Inside uniform sphere, field varies linearly with r.

Final Answer: At centre field is zero.

IB Question 7

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

IB Question 8

Question: Find variation of g at height h.

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

IB Question 9

Question: Find orbital speed of satellite.

Show Solution

Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

IB Question 10

Question: Find escape speed from a planet.

Show Solution

Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

IGCSE Questions

IGCSE Question 1

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

IGCSE Question 2

Question: Find variation of g at height h.

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

IGCSE Question 3

Question: Find orbital speed of satellite.

Show Solution

Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

IGCSE Question 4

Question: Find escape speed from a planet.

Show Solution

Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

IGCSE Question 5

Question: Use Kepler's third law for period ratio.

Show Solution

Formula/Concept: T² proportional to r³

Solution: T ratio equals radius ratio to the power 3/2.

Final Answer: Same central mass.

IGCSE Question 6

Question: Find field inside solid sphere.

Show Solution

Formula/Concept: E = GMr/R³

Solution: Inside uniform sphere, field varies linearly with r.

Final Answer: At centre field is zero.

IGCSE Question 7

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

IGCSE Question 8

Question: Find variation of g at height h.

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

IGCSE Question 9

Question: Find orbital speed of satellite.

Show Solution

Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

IGCSE Question 10

Question: Find escape speed from a planet.

Show Solution

Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

A-Level Questions

A-Level Question 1

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

A-Level Question 2

Question: Find variation of g at height h.

Show Solution

Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

A-Level Question 3

Question: Find orbital speed of satellite.

Show Solution

Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

A-Level Question 4

Question: Find escape speed from a planet.

Show Solution

Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

A-Level Question 5

Question: Use Kepler's third law for period ratio.

Show Solution

Formula/Concept: T² proportional to r³

Solution: T ratio equals radius ratio to the power 3/2.

Final Answer: Same central mass.

A-Level Question 6

Question: Find field inside solid sphere.

Show Solution

Formula/Concept: E = GMr/R³

Solution: Inside uniform sphere, field varies linearly with r.

Final Answer: At centre field is zero.

A-Level Question 7

Question: Find gravitational force when two point masses are given.

Show Solution

Formula/Concept: F = Gm₁m₂/r²

Solution: Substitute masses and centre distance. Keep SI units.

Final Answer: Use Newton.

A-Level Question 8

Question: Find variation of g at height h.

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Formula/Concept: g_h = g(R/(R+h))²

Solution: Put given height and simplify the ratio.

Final Answer: Use centre distance.

A-Level Question 9

Question: Find orbital speed of satellite.

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Formula/Concept: v = √(GM/r)

Solution: Use r = R+h if height is given.

Final Answer: Do not use h alone.

A-Level Question 10

Question: Find escape speed from a planet.

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Formula/Concept: v_e = √(2GM/R)

Solution: Apply energy conservation from surface to infinity.

Final Answer: Mass cancels.

Assertion Reason

Assertion Reason 1

Assertion: Escape velocity is independent of projectile mass. Reason: Mass cancels in energy equation.

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Answer: Both statements are true, and the reason explains the assertion.

Exam Note: Read whether the reason explains the assertion, not only whether both are true.

Assertion Reason 2

Assertion: Inside a thin spherical shell, gravitational field is zero. Reason: Potential inside shell is constant.

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Answer: Both statements are true, and the reason explains the assertion.

Exam Note: Read whether the reason explains the assertion, not only whether both are true.

Assertion Reason 3

Assertion: A geostationary satellite has period 24 h. Reason: It must match Earth's rotation.

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Answer: Both statements are true, and the reason explains the assertion.

Exam Note: Read whether the reason explains the assertion, not only whether both are true.

Assertion Reason 4

Assertion: A planet moves faster near perihelion. Reason: Areal velocity is constant.

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Answer: Both statements are true, and the reason explains the assertion.

Exam Note: Read whether the reason explains the assertion, not only whether both are true.

Assertion Reason 5

Assertion: Satellite total energy is negative. Reason: It is gravitationally bound.

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Answer: Both statements are true, and the reason explains the assertion.

Exam Note: Read whether the reason explains the assertion, not only whether both are true.

Assertion Reason 6

Assertion: Escape velocity is independent of projectile mass. Reason: Mass cancels in energy equation.

Show Solution

Answer: Both statements are true, and the reason explains the assertion.

Exam Note: Read whether the reason explains the assertion, not only whether both are true.

Assertion Reason 7

Assertion: Inside a thin spherical shell, gravitational field is zero. Reason: Potential inside shell is constant.

Show Solution

Answer: Both statements are true, and the reason explains the assertion.

Exam Note: Read whether the reason explains the assertion, not only whether both are true.

Assertion Reason 8

Assertion: A geostationary satellite has period 24 h. Reason: It must match Earth's rotation.

Show Solution

Answer: Both statements are true, and the reason explains the assertion.

Exam Note: Read whether the reason explains the assertion, not only whether both are true.

Assertion Reason 9

Assertion: A planet moves faster near perihelion. Reason: Areal velocity is constant.

Show Solution

Answer: Both statements are true, and the reason explains the assertion.

Exam Note: Read whether the reason explains the assertion, not only whether both are true.

Assertion Reason 10

Assertion: Satellite total energy is negative. Reason: It is gravitationally bound.

Show Solution

Answer: Both statements are true, and the reason explains the assertion.

Exam Note: Read whether the reason explains the assertion, not only whether both are true.

Assertion Reason 11

Assertion: Escape velocity is independent of projectile mass. Reason: Mass cancels in energy equation.

Show Solution

Answer: Both statements are true, and the reason explains the assertion.

Exam Note: Read whether the reason explains the assertion, not only whether both are true.

Assertion Reason 12

Assertion: Inside a thin spherical shell, gravitational field is zero. Reason: Potential inside shell is constant.

Show Solution

Answer: Both statements are true, and the reason explains the assertion.

Exam Note: Read whether the reason explains the assertion, not only whether both are true.

Assertion Reason 13

Assertion: A geostationary satellite has period 24 h. Reason: It must match Earth's rotation.

Show Solution

Answer: Both statements are true, and the reason explains the assertion.

Exam Note: Read whether the reason explains the assertion, not only whether both are true.

Assertion Reason 14

Assertion: A planet moves faster near perihelion. Reason: Areal velocity is constant.

Show Solution

Answer: Both statements are true, and the reason explains the assertion.

Exam Note: Read whether the reason explains the assertion, not only whether both are true.

Assertion Reason 15

Assertion: Satellite total energy is negative. Reason: It is gravitationally bound.

Show Solution

Answer: Both statements are true, and the reason explains the assertion.

Exam Note: Read whether the reason explains the assertion, not only whether both are true.

Case Study Questions

Case Study 1

Question: A satellite is revolving around Earth in circular orbit of radius r. Discuss speed, time period and energy.

Show Solution

Formula/Concept: v = √(GM/r), T = 2π√(r³/GM), E = -GMm/2r

Solution: Use circular motion and gravitational force as centripetal force. Energy remains negative for a bound satellite.

Final Answer: Bound circular orbit

Case Study 2

Question: A planet moves in elliptical orbit around Sun and sweeps equal areas in equal times.

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Formula/Concept: Kepler's second law

Solution: Areal velocity remains constant. Near Sun speed is higher; far from Sun speed is lower.

Final Answer: Angular momentum is conserved

Case Study 3

Question: A body is projected from Earth with escape velocity.

Show Solution

Formula/Concept: v_e = √(2gR)

Solution: Initial kinetic energy equals energy required to reach infinity with zero speed.

Final Answer: Total energy at threshold is zero

Case Study 4

Question: A point lies inside a thin spherical shell.

Show Solution

Formula/Concept: Field inside shell is zero

Solution: Net gravitational attraction cancels at every point inside a uniform shell.

Final Answer: E = 0

Quick Revision Notes

Must Remember

Gravity is always attractive.
G is universal, g depends on planet and position.
Potential is negative with zero at infinity.
Field is negative potential gradient.

Common Traps

Use r = R+h for satellite problems.
Do not use height h in place of orbital radius.
Inside solid sphere: g proportional to r.
Inside shell: g = 0.

Exam Strategy

Write formula first.
Check units.
For ratios, cancel constants early.
For vectors, draw directions before resolving.

Need guided practice? For Gravitation formulae, NCERT exercises, PYQs and NEET/JEE problem solving, contact Kumar Sir.

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