Acceleration due to Gravity & Weight

• g — acceleration due to gravity near Earth's surface ≈ 9.8 m/s² (NCERT often uses 10 m/s²).
• Relation — g = GM/R² (M = Earth mass, R = Earth radius).
• Weight W = mg (force of gravity on a body); mass m stays constant.
• Weight varies with location; mass does not.

1. Weight — W = mg; SI unit newton (N).
2. Mass — amount of matter; kg; invariant.
3. g on Earth — ≈ 9.8 m/s²; at poles slightly higher, equator slightly lower (rotation effect — intro).
4. g on Moon — about 1/6 of Earth's g (less mass, smaller radius).
5. Free fall — all objects fall with same g (ignoring air resistance).
6. Diagram (text) — spring balance reads weight; beam balance compares masses.
7. NCERT Ch. 10 — difference between mass and weight; weighing on Moon.
8. Real world — astronauts 'weightless' in orbit (free fall); kg vs N on grocery labels.

Finding weight of a 50 kg student on Earth (g = 10 m/s²) and on Moon (g ≈ 1.6 m/s²)

Given: m = 50 kg
Step 1 — Earth: W = mg = 50 × 10 = 500 N
Step 2 — Moon: W = 50 × 1.6 = 80 N
Step 3 — Mass remains 50 kg on both.
Step 4 — Spring balance shows 500 N on Earth; beam balance still needs 50 kg mass to balance.

• Using kg for weight (kg is mass; weight in N).
• Misconception: mass changes on Moon (only weight changes).
• Confusing g (m/s²) with G (N·m²/kg²).
• Thinking heavier objects fall faster in air (air resistance, not g).
• Equating density with mass.

• Distinguish mass and weight with units.
• Calculate weight of 2 kg object when g = 9.8 m/s².
• Why does a spring balance measure weight, not mass?
• Where would you weigh more: pole or equator? (qualitative)

Open the Practice tab for graded questions on Acceleration due to Gravity & Weight.