Is it correct to say: Confusing G (universal constant) with g (acceleration)?

G = 6.67 × 10⁻¹¹ N·m²/kg² — SAME everywhere in the universe. g ≈ 9.8 m/s² — LOCAL acceleration, varies with planet, altitude, latitude.

Is it correct to say: Treating mass and weight as the same?

Mass (kg): scalar, constant. Weight (N): force = mg, varies with g. On the Moon your mass is unchanged but weight is 1/6.

Is it correct to say: Writing weight in kg?

Weight is a force ⇒ unit newton (N). '60 kg-wt' is an older engineering shortcut equal to 60 × 9.8 = 588 N.

Is it correct to say: Using r in km inside F = GMm/r² without converting?

Convert all lengths to metres before substituting. 6400 km = 6.4 × 10⁶ m.

Is it correct to say: Thinking heavier objects fall faster?

In vacuum all objects fall with the SAME g regardless of mass (Galileo). Air resistance is what makes feathers fall slower in air.

Is it correct to say: Using r = R (Earth's radius) inside v_orb for a high satellite?

r = R + h from Earth's centre. For geostationary orbit r ≈ 42,000 km, not 6400 km.

Gravitation

Universal law of gravitation, acceleration due to gravity, weight vs mass, orbital and escape velocity, Kepler's laws — Maharashtra SSC Class 10 Science-1 Ch 1

📐 9 formulas✏️ 3 examples🎯 6 practice⚖️ 5-6 marks🏫 Maharashtra State Board📚 Class 10✓ 2025–26 syllabus

💡

Board Exam Tips

→Universal law of gravitation derivation from Kepler's third law — 4-mark question every year.
→Numerical on F = GMm/r² OR g = GM/R² using standard Earth data — 3 marks.
→Escape velocity derivation (½mv² = GMm/R) — 3-mark HOTS favourite.
→Difference between mass and weight — 2 marks, do NOT confuse units (kg vs N).
→Kepler's three laws in one line each — 3 marks safe.

📊 Diagram

Two masses attracting each other along the line joining their centres — force vector diagram

📐 Formulas(9)

Universal Law of Gravitation (Newton, 1687)★ Board fav

F = G \frac{m _{1} m _{2}}{r ^{2}}

Symbol	Meaning
$F$	Gravitational force (N)
$G$	Universal gravitational constant = 6.67 × 10⁻¹¹ N·m²/kg²
$m_{1}, m_{2}$	Masses of the two bodies (kg)
$r$	Distance between their centres (m)

Acceleration due to Gravity (surface)★ Board fav

g = \frac{GM}{R ^{2}}

Symbol	Meaning
$g$	Acceleration due to gravity (m/s²)
$M$	Mass of Earth ≈ 6 × 10²⁴ kg
$R$	Radius of Earth ≈ 6.4 × 10⁶ m

Weight★ Board fav

W = m g

Symbol	Meaning
$W$	Weight (N)
$m$	Mass (kg) — scalar, constant everywhere
$g$	Local acceleration due to gravity (m/s²)

g at Altitude h

g_{h} = g (\frac{R}{R + h})^{2}

Orbital Velocity

v_{orb} = \frac{GM}{r}

Symbol	Meaning
$v_{o} r b$	Orbital velocity (m/s)
$r$	Orbital radius from Earth's centre (m)

Escape Velocity★ Board fav

v_{e} = \frac{2 GM}{R} = 2 g R

Symbol	Meaning
$v_{e}$	Escape velocity (m/s)
$R$	Radius of Earth (m)

Kepler's First Law (orbits)

Each planet moves in an ellipse with the Sun at one focus

Kepler's Second Law (equal areas)

\frac{d A}{d t} = constant

Kepler's Third Law (period-radius)★ Board fav

T^{2} \propto r^{3} i.e. \frac{T ^{2}}{r ^{3}} = \frac{4 π ^{2}}{GM}

✏️ Solved Examples

1Solved Exampleeasy4 steps

Find the gravitational force between Earth (M = 6 × 10²⁴ kg) and a person of mass 70 kg standing on its surface. Take G = 6.67 × 10⁻¹¹ N·m²/kg² and R = 6.4 × 10⁶ m.

List known values in SI units

G = 6.67 \times 1 0^{- 11}, M = 6 \times 1 0^{24}, m = 70, R = 6.4 \times 1 0^{6}

2Solved Exampleboard4 steps

The mass of an astronaut is 60 kg. Find her weight (a) on Earth (g = 9.8 m/s²) and (b) on the Moon (g_m = 1.6 m/s²). What is her mass on the Moon?

Mass is a scalar and remains the same everywhere.

m_{Moon} = m_{Earth} = 60 kg

3Solved ExampleHOTS5 steps

Derive the escape velocity for Earth and compute its value. Then explain why the Moon has no atmosphere while Earth does.

For a projectile to just escape, kinetic energy at surface = gravitational potential energy magnitude

\frac{1}{2} m v_{e}^{2} = \frac{GM m}{R}

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6

1
Confusing G (universal constant) with g (acceleration)
✓G = 6.67 × 10⁻¹¹ N·m²/kg² — SAME everywhere in the universe. g ≈ 9.8 m/s² — LOCAL acceleration, varies with planet, altitude, latitude.
2
Treating mass and weight as the same
✓Mass (kg): scalar, constant. Weight (N): force = mg, varies with g. On the Moon your mass is unchanged but weight is 1/6.
3
Writing weight in kg
✓Weight is a force ⇒ unit newton (N). '60 kg-wt' is an older engineering shortcut equal to 60 × 9.8 = 588 N.
4
Using r in km inside F = GMm/r² without converting
✓Convert all lengths to metres before substituting. 6400 km = 6.4 × 10⁶ m.
5
Thinking heavier objects fall faster
✓In vacuum all objects fall with the SAME g regardless of mass (Galileo). Air resistance is what makes feathers fall slower in air.
6
Using r = R (Earth's radius) inside v_orb for a high satellite
✓r = R + h from Earth's centre. For geostationary orbit r ≈ 42,000 km, not 6400 km.

🎯 Practice Yourself

🎯Practice Yourself6 questions

Q1
Two masses of 100 kg each are placed 1 m apart. Find the gravitational force between them.
$F = G \frac{100 \times 100}{1 ^{2}}$
Q2
The Moon revolves around the Earth in about 27.3 days. The mean orbital radius is 3.84 × 10⁸ m. Use Kepler's third law to check that GM_Earth ≈ 4 × 10¹⁴ m³/s².
Q3
An object weighs 49 N on Earth. What is its mass?
$m = \frac{W}{g} = \frac{49}{9.8}$
Q4
Calculate the value of g on the surface of Mars. Take M_Mars = 6.4 × 10²³ kg and R_Mars = 3.4 × 10⁶ m.
Q5
The escape velocity from Earth is 11.2 km/s. What is the orbital velocity of a satellite just above Earth's surface?
Q6
State any two consequences of the fact that g varies with height.

📝 Notes

Gravitation — Maharashtra Board Class 10

The Universal Law of Gravitation (Newton, 1687) states that every object in the universe attracts every other object with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

Key numbers to remember

G = 6.67 × 10⁻¹¹ N·m²/kg² (universal, same everywhere).
Earth: M ≈ 6 × 10²⁴ kg, R ≈ 6.4 × 10⁶ m.
g at Earth's surface ≈ 9.8 m/s².
Escape velocity from Earth ≈ 11.2 km/s.
Orbital velocity just above surface ≈ 7.9 km/s.

Mass vs weight

| Property | Mass | Weight | |---|---|---| | Nature | Scalar — quantity of matter | Vector — gravitational force | | Unit | kg | newton (N) | | Depends on location? | No | Yes (via g) | | On the Moon | Same | 1/6 of Earth |

How g varies

With altitude h: g_h = g (R/(R+h))². Falls with height.
With depth d: g_d = g (1 − d/R). Falls to zero at Earth's centre.
At the poles slightly greater than at the equator (Earth's flattening + rotation).