Study Notes: Gravitation (SOF NSO)

Overview

Gravitation is a fundamental force that governs the motion of celestial bodies and falling objects on Earth. For SOF NSO Class 9-10, this topic carries significant weight as it bridges everyday observations (objects falling, weight on a scale) with universal physical laws. Students must master Newton's universal law of gravitation, understand the distinction between mass and weight, explain free fall motion, and apply thrust-pressure concepts to solve numerical problems.

The topic appears regularly in NSO papers through numerical problems (calculating gravitational force, weight on different planets), conceptual MCQs (why astronauts feel weightless), and application-based questions (pressure variations in fluids). Strong command over formulas, unit conversions, and the inverse-square relationship is essential. The Achievers Section often tests this topic through multi-step problems combining gravitation with motion or energy concepts.

Key Concepts

• **Universal Law of Gravitation**: 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 centers. This explains planetary orbits, tides, and why objects fall to Earth.

• **Gravitational Constant (G)**: The value 6.67 × 10⁻¹¹ N m²/kg² is a universal constant. It remains the same everywhere in the universe, unlike acceleration due to gravity (g) which varies with location.

• **Free Fall**: Motion of an object under the sole influence of gravity (ignoring air resistance). All objects, regardless of mass, fall with the same acceleration g = 9.8 m/s² near Earth's surface.

• **Mass vs Weight**: Mass is the amount of matter in an object (scalar, measured in kg, constant everywhere). Weight is the gravitational force on an object (vector, measured in newtons, varies with location).

• **Acceleration due to Gravity (g)**: On Earth's surface g ≈ 9.8 m/s² or 10 m/s² (for quick calculations). It decreases with altitude and differs on other planets/moons based on their mass and radius.

• **Thrust and Pressure**: Thrust is the perpendicular force acting on a surface. Pressure is thrust per unit area. Fluids (liquids and gases) exert pressure in all directions; pressure increases with depth in a liquid column.

Formulas / Key Facts

**F = G(m₁m₂)/r²** — Universal law of gravitation. F is force in newtons, m₁ and m₂ are masses in kg, r is distance between centers in meters, G = 6.67 × 10⁻¹¹ N m²/kg².

**Weight W = mg** — Weight in newtons equals mass (kg) times acceleration due to gravity (m/s²). On Earth, W = m × 9.8.

**g = GM/R²** — Acceleration due to gravity at a planet's surface. M is planet's mass, R is radius, G is gravitational constant.

**Equations of motion for free fall**: v = u + gt, s = ut + ½gt², v² = u² + 2gs. Here u = initial velocity, v = final velocity, t = time, s = distance, g = 9.8 m/s².

**Pressure P = Thrust/Area = F/A** — Measured in pascals (Pa) or N/m². 1 Pa = 1 N/m².

**Liquid pressure P = ρgh** — Pressure at depth h in a liquid of density ρ. ρ = density (kg/m³), g = 9.8 m/s², h = depth (m).

**Weight on Moon = (1/6) × Weight on Earth** — Moon's gravity is approximately 1/6th of Earth's.

**Thrust is perpendicular force** — Pressure depends on both thrust and contact area; smaller area → higher pressure.

Worked Examples

**Example 1: Gravitational Force Between Two Objects**

Two spheres of mass 50 kg and 100 kg are placed 2 m apart. Calculate the gravitational force between them.

**Solution**:

• Given: m₁ = 50 kg, m₂ = 100 kg, r = 2 m, G = 6.67 × 10⁻¹¹ N m²/kg²
• Formula: F = G(m₁m₂)/r²
• F = (6.67 × 10⁻¹¹ × 50 × 100)/(2)²
• F = (6.67 × 10⁻¹¹ × 5000)/4
• F = 3.335 × 10⁻⁸/4 = 8.34 × 10⁻⁹ N

**Example 2: Weight on Different Planets**

A student has mass 60 kg on Earth. Calculate her weight on Earth and on Mars (g_Mars = 3.7 m/s²).

**Solution**:

• Weight on Earth: W = mg = 60 × 9.8 = 588 N
• Weight on Mars: W = mg = 60 × 3.7 = 222 N
• Note: Mass remains 60 kg on both planets; only weight changes.

**Example 3: Pressure Calculation**

A brick of weight 30 N has dimensions 20 cm × 10 cm × 5 cm. Find the maximum and minimum pressure it can exert.

**Solution**:

• Maximum pressure occurs when area is minimum (smallest face)
• Minimum area = 10 cm × 5 cm = 50 cm² = 50 × 10⁻⁴ m² = 0.005 m²
• P_max = 30/0.005 = 6000 Pa
• Maximum area = 20 cm × 10 cm = 200 cm² = 0.02 m²
• P_min = 30/0.02 = 1500 Pa

Common Mistakes

**Confusing mass and weight** → Mass is constant everywhere (kg), weight changes with gravity (N). On the Moon, your mass stays the same but weight becomes 1/6th. Always use W = mg for weight calculations.

**Forgetting to square the distance** → The formula is F = Gm₁m₂/r², not F = Gm₁m₂/r. Doubling the distance makes force ¼ as strong, not ½.

**Using wrong units** → Distance must be in meters (not cm or km), mass in kg (not grams). Convert before substituting. Area for pressure must be in m², not cm².

**Thinking heavier objects fall faster** → In free fall (no air resistance), all objects accelerate at g = 9.8 m/s² regardless of mass. A feather and hammer fall together in vacuum.

**Adding pressure from multiple sides** → Liquid pressure at a depth acts equally in all directions, but for calculations use P = ρgh once for a given depth. Don't multiply by number of sides.

Quick Reference

• **F = G(m₁m₂)/r²** with G = 6.67 × 10⁻¹¹ N m²/kg² — universal gravitation
• **W = mg** where g = 9.8 m/s² on Earth — weight formula
• **g on Moon = g on Earth ÷ 6** — remember the 1/6 ratio
• Free fall: all objects fall at same rate (9.8 m/s²), independent of mass
• **Pressure = Force/Area** — smaller area means higher pressure
• **P = ρgh** for liquid pressure — depends on depth, density, not container shape