Complete Solutions and Summary of Gravitation – NCERT Class 9, Science, Chapter 9 – Summary, Questions, Answers, Extra Questions
Detailed summary and explanation of Chapter 9 ‘Gravitation’ with all question answers, extra questions, and solutions from NCERT Class IX, Science.
Updated: 3 weeks ago
Categories: NCERT, Class IX, Science, Summary, Extra Questions, Gravitation, Chapter 9
Tags: Gravitation, Universal Law of Gravitation, Free Fall, Acceleration due to Gravity, Mass, Weight, Thrust, Pressure, Buoyancy, Archimedes’ Principle, Class 9, NCERT, Science, Chapter 9, Answers, Extra Questions
Gravitation
Chapter 9: Science - Complete Study Guide
Chapter Overview
F ∝ Mm/d²
Universal Law
g = 9.8 m/s²
Acceleration
W = mg
Weight
1/6 Earth
Moon Weight
What You'll Learn
Gravitational Force
Universal attraction between masses.
Free Fall
Motion under gravity alone.
Mass vs Weight
Mass constant, weight varies.
Buoyancy
Upthrust in fluids, Archimedes.
Key Highlights
Gravitation explains planetary motion, free fall, and buoyancy. Newton's law: force proportional to masses, inverse square distance. Acceleration g=9.8 m/s² near Earth. Weight W=mg varies by location; mass m constant. Thrust/area=pressure; fluids transmit pressure. Buoyant force equals displaced fluid weight, explains floating/sinking.
Comprehensive Chapter Summary
9.1 Gravitation
- Objects in motion require force to change speed or direction; dropped objects fall to Earth due to gravitational force.
- Planets orbit Sun, Moon orbits Earth, all due to same gravitational force acting on them.
- Newton realized the force pulling apple to Earth also keeps Moon in orbit; Moon "falls" towards Earth but moves tangentially.
- Activity 9.1: Whirling stone on thread shows centripetal force (center-seeking) keeps it in circular path; release shows tangent motion.
- Without centripetal force from Earth's gravity, Moon would fly off in straight line; explains orbital motion.
- Apple attracts Earth per Newton's third law, but Earth's mass so large, acceleration negligible (second law: a=F/m).
- Same for Moon-Earth; negligible Earth motion due to mass difference.
- All objects in universe attract each other with gravitational force; explains solar system orbits.
- Gravitational force weak unless large masses involved; not felt between small objects like friends.
- Extends to all celestial and terrestrial bodies, universal in scope.
- Inverse-square: If distance doubles, force quarters; if halved, force quadruples.
- Activity demonstrates circular motion acceleration towards center.
- Newton's insight from apple fall to Moon orbit unified phenomena.
Centripetal Force in Orbit
Moon's orbital path requires constant inward pull from Earth; without gravity, straight-line motion. Tangent line touches circle at one point.
9.1.1 Universal Law of Gravitation
- Every object attracts another with force proportional to product of masses, inversely to square of distance between centers.
- Formula: \[ F = G \frac{M m}{d^2} \], where G is universal constant (6.67 × 10^{-11} Nm²/kg²).
- Force along line joining centers; G from Cavendish experiment using torsion balance.
- Example 9.1: Earth-Moon force: M=6×10^{24}kg, m=7.4×10^{22}kg, d=3.84×10^8m, F=2.02×10^{20}N.
- From \[ F d^2 = G M m \], derive G = F d² / (M m).
- SI unit Nm²/kg²; value small, explains weak everyday forces.
- Compute force between nearby friends: negligible due to small masses.
- Law universal: applies to all bodies, big/small, celestial/terrestrial.
- Example calculation shows precise application to astronomical bodies.
- Proportionality: F ∝ M m, F ∝ 1/d²; combines to inverse-square law.
- Henry Cavendish (1731-1810) measured G experimentally.
Universal Law Formula
- \[ F \propto M \times m \]
- \[ F \propto \frac{1}{d^2} \]
- \[ F = G \frac{M m}{d^2} \]
Importance
- Binds to Earth
- Moon orbit
- Planets around Sun
- Tides from Moon/Sun
Example: Earth-Moon Attraction
Using G=6.7×10^{-11}, masses, distance yields 2.02×10^{20}N; symmetric force per third law.
9.2 Free Fall
- Free fall: Object falls under gravity alone; acceleration g due to Earth's pull.
- Activity 9.2: Thrown stone rises then falls; velocity changes magnitude, direction constant downward.
- Change in velocity = acceleration; g in m/s², same as acceleration unit.
- From second law, F = m g; gravitational force F = G M m / d², so g = G M / d².
- Near Earth surface, d ≈ R (radius), so \[ g = \frac{G M}{R^2} \] ≈ 9.8 m/s².
- Example 9.2: Car falls 0.5s, g=10 m/s²: v=5 m/s, avg speed=2.5 m/s, height=1.25m.
- Equations: v=u+at, s=ut+(1/2)at², v²=u²+2as; a=±g (down +ve).
- Example 9.3: Object to 10m height: u=14 m/s, t=1.43s upward.
- Activity 9.3: Paper falls slower than stone due to air resistance; vacuum equal rate.
- All objects fall same rate in vacuum; g independent of mass.
- Galileo demonstrated from Leaning Tower of Pisa.
- Earth not perfect sphere; g greater at poles than equator due to radius variation.
- For distant objects, g = G M / d² varies.
- To calculate g: G=6.7×10^{-11}, M=6×10^{24}kg, R=6.4×10^6m yields 9.8 m/s².
Free Fall Equations
- \[ v = u + gt \]
- \[ s = ut + \frac{1}{2} g t^2 \]
- \[ v^2 = u^2 + 2 g s \]
Positive g downward; independent of mass.
Vacuum Drop Activity
Paper and stone fall equally without air; proves g uniform for all masses.
9.3 Mass and 9.4 Weight
- Mass m: Measure of inertia; constant everywhere (Earth, Moon, space).
- Greater mass, greater inertia; from previous chapter.
- Weight W: Force of attraction by Earth; W = m g, in newtons (N).
- Vertical downward; depends on location via g.
- At given place, W ∝ m; used to measure mass locally.
- 9.4.1 Weight on Moon: Moon mass 1/81 Earth, radius 1/3.7, so g_m = g_e /6.
- W_m = (1/6) W_e; from \[ W = \frac{G M m}{R^2} \].
- Example 9.4: 10kg on Earth, W=98N (g=9.8).
- Example 9.5: 10N on Earth, 1.67N on Moon.
- Mass constant, weight varies; explains scale differences on planets.
- Table 9.1: Earth M=5.98×10^{24}kg, R=6.37×10^6m; Moon 7.36×10^{22}kg, 1.74×10^6m.
- Calculations: W_m / W_e = (M_m / M_e) × (R_e / R_m)^2 ≈ 1/6.
- Weight as gravitational force; direction downward.
Mass vs Weight
Mass: Inertia measure, invariant. Weight: mg, location-dependent; Moon 1/6th due to smaller g.
9.5 Thrust and Pressure
- Thrust: Net force perpendicular to surface (e.g., weight on sand).
- Pressure: Thrust/area; explains camel tracks, tank chains, wide tires, sharp tools.
- SI unit: Pa (N/m²); named after Pascal.
- Situation 1: Pin head large area (low pressure on thumb), tip small (high on board).
- Situation 2: Standing on sand (small foot area, high pressure, sinks); lying (large area, low pressure).
- Example 9.6: 5kg wood block (49N thrust): 20×10cm side=2450 Pa; 40×20cm=612.5 Pa.
- Smaller area, higher pressure; explains nails, knives, foundations.
- 9.5.1 Pressure in Fluids: Liquids/gases exert pressure due to weight; transmitted undiminished all directions (Pascal's law).
- Solids exert via weight; fluids on base/walls.
- Confined fluid pressure equal in all directions.
Pressure Formula
\[ P = \frac{F}{A} \] (Thrust F, Area A); Pa = N/m².
Fluid Pressure
Transmitted equally; basis for hydraulics.
9.5.2 Buoyancy and 9.5.3 Float/Sink
- Activity 9.4: Empty bottle floats, push feels upward force (buoyancy/upthrust); increases with immersion.
- Release: Bounces up as upthrust > weight.
- To immerse: Downward force = upthrust - weight.
- Buoyancy: Upward force by fluid; depends on fluid density.
- Activity 9.5: Iron nail sinks (weight > upthrust); cork floats (upthrust > weight).
- Density: Mass/volume; low density floats, high sinks in fluid.
- Cork density < water, floats; nail > water, sinks.
- Activity 9.6: Stone on string/balance; immersion decreases extension/reading (upthrust reduces net downward force).
- No further change when fully immersed.
Buoyancy Activity
Bottle push shows increasing upthrust; ship floats as displaced water weight = ship weight.
9.6 Archimedes’ Principle
- Upward buoyant force = weight of fluid displaced by object (fully/partially immersed).
- Explains Activity 9.7: Extension decrease = buoyant force magnitude.
- Full immersion: Constant displacement, constant force.
- Applies to all fluids; magnitude same for given body in same fluid, varies by density.
- Archimedes discovered via bathtub overflow; "Eureka!" for crown purity.
- Applications: Ship/submarine design, lactometers (milk purity), hydrometers (liquid density).
- Objects float if density < fluid (upthrust > weight); sink if >.
- Why plastic block rises: Density < water, upthrust > weight.
- 50g substance, 20cm³: Density=2.5 g/cm³ >1, sinks.
- 500g packet, 350cm³: Density≈1.43 >1, sinks; displaces 350g water.
- Principle unifies buoyancy phenomena.
Archimedes' Eureka
Bathtub overflow = displaced water weight; tested crown volume vs gold.
Key Concepts and Definitions
Gravitation
Universal attraction force.
Universal Law
\[ F = G \frac{Mm}{d^2} \]
Free Fall
Under gravity alone, a=g.
Weight
W=mg, varies by g.
Mass
Inertia measure, constant.
Pressure
F/A, in Pa.
Buoyancy
Upthrust = displaced weight.
Important Facts
G=6.67×10^{-11}
Constant
R=6.4×10^6m
Earth Radius
M=6×10^{24}kg
Earth Mass
1/6
Moon g
Archimedes
Buoyancy
Questions and Answers from Chapter
Short Questions (1 Mark)
Q1. State the universal law of gravitation.
Answer: Force proportional to product of masses, inversely to square of distance.
Q2. Write the formula for gravitational force between Earth and surface object.
Answer: \[ F = \frac{G M m}{R^2} \]
Q3. What is free fall?
Answer: Fall under gravity alone.
Q4. What is acceleration due to gravity?
Answer: g ≈ 9.8 m/s².
Q5. What is mass of an object?
Answer: Measure of inertia, constant.
Q6. What is weight?
Answer: W = mg.
Q7. Why weight on Moon 1/6th Earth?
Answer: Smaller g_m.
Q8. What is thrust?
Answer: Force perpendicular to surface.
Q9. What is pressure?
Answer: Thrust/area.
Q10. What is buoyancy?
Answer: Upward force in fluid.
Q11. Why objects float/sink?
Answer: Density vs fluid.
Q12. State Archimedes' principle.
Answer: Buoyant force = displaced fluid weight.
Q13. What is centripetal force?
Answer: Center-seeking in circular motion.
Q14. Value of G?
Answer: 6.67 × 10^{-11} Nm²/kg².
Q15. Unit of g?
Answer: m/s².
Q16. Why paper falls slower?
Answer: Air resistance.
Q17. Difference mass/weight?
Answer: Mass constant, weight varies.
Q18. SI unit of pressure?
Answer: Pa (N/m²).
Q19. Why ship floats?
Answer: Displaced water weight = ship weight.
Q20. Direction of buoyant force?
Answer: Upward.
Medium Questions (3 Marks)
Q1. Importance of universal law of gravitation?
Answer: Explains binding to Earth, Moon orbit, planets around Sun, tides. Unifies phenomena.
Q2. Differences between mass and weight?
Answer: Mass: Inertia, constant, kg. Weight: mg, varies, N, downward force.
Q3. Why weight on Moon 1/6th Earth?
Answer: g_m = g_e (M_m R_e²)/(M_e R_m²) ≈1/6; smaller Moon mass/radius.
Q4. What is free fall? Acceleration?
Answer: Fall under gravity alone; g= G M / R² =9.8 m/s², independent of mass.
Q5. Why heavy object not fall faster?
Answer: g same for all; air resistance negligible in vacuum.
Q6. What is thrust and pressure?
Answer: Thrust: Perpendicular force. Pressure: F/A; explains wide tires low pressure.
Q7. Why difficult thin strap bag?
Answer: Small area, high pressure on shoulder.
Q8. What is buoyancy?
Answer: Upward force by fluid; increases with immersion depth.
Q9. Why object float/sink in water?
Answer: Float if density <1 g/cm³ (upthrust > weight); sink if >.
Q10. State Archimedes' principle.
Answer: Buoyant force = weight of displaced fluid; explains floating.
Q11. How force changes if distance halved?
Answer: F becomes 4 times (inverse square).
Q12. Gravitational force on all proportional to mass; why not faster fall?
Answer: Acceleration g independent of mass; F=mg, a=g.
Q13. Magnitude of Earth-1kg force?
Answer: ≈9.8N (weight).
Q14. Earth attract Moon same/greater/smaller?
Answer: Same; third law action-reaction equal.
Q15. Why Earth not move to Moon?
Answer: Large Earth mass, small acceleration.
Q16. Force if one mass doubled?
Answer: Doubles.
Q17. Force if distance doubled/tripled?
Answer: Halves/1/9th.
Q18. Both masses doubled?
Answer: Quadruples.
Q19. Acceleration of free fall?
Answer: g=9.8 m/s² downward.
Q20. Gravitational force Earth-object called?
Answer: Weight.
Long Questions (6 Marks)
Q1. How force of gravitation changes if distance reduced to half?
Answer: Law: F ∝ 1/d²; half d → d' = d/2, F' = G Mm /(d/2)² = 4 G Mm / d² =4F. Increases fourfold; explains stronger pull closer. Example: Halve Earth-Moon distance, force quadruples, disrupting orbit.
Q2. Gravitational force proportional to masses; why heavy not fall faster?
Answer: F= G M m / R² = m g, so a = F/m = g, independent of m. All accelerate at g=9.8 m/s² in vacuum. Air resistance affects light objects more, but ideally equal. Galileo proved; equations v=gt, s=(1/2)gt² apply uniformly.
Q3. Magnitude gravitational force Earth-1kg object surface? (M=6×10^{24}kg, R=6.4×10^6m)
Answer: F= G M m / R², G=6.67×10^{-11}, m=1kg: F= (6.67×10^{-11})(6×10^{24})(1) / (6.4×10^6)² ≈9.8N. Equals weight; derives g= G M / R²=9.8 m/s².
Q4. Earth-Moon attraction: greater/smaller/same? Why?
Answer: Same magnitude, opposite directions (third law). F= G M m / d² symmetric in M,m. Earth larger mass, but force equal; Moon accelerates more (a=F/m), orbits Earth.
Q5. If Moon attracts Earth, why no move towards Moon?
Answer: Equal force, but a= F/M_earth small (M_earth >> M_moon); a_moon large. Earth "wobbles" slightly, but negligible. Second law: acceleration inverse to mass.
Q6. Force changes if: (i) one mass doubled? (ii) distance doubled/tripled? (iii) both doubled?
Answer: (i) F' =2F (∝ m). (ii) Doubled: F'=F/4; tripled: F'=F/9 (∝1/d²). (iii) F'=4F (∝ M m). Law F= G M m / d²; proportionalities direct.
Q7. Importance universal law gravitation?
Answer: Explains: (i) Earth binding, (ii) Moon orbit (centripetal=gravity), (iii) planetary/Sun motion, (iv) tides (Moon/Sun pull). Unifies celestial mechanics; predicts orbits, enables space travel.
Q8. Acceleration free fall?
Answer: g=9.8 m/s² downward; from g= G M / R². Uniform near Earth; equations for motion: v=gt (u=0), s=(1/2)gt². Independent mass; vacuum equal fall.
Q9. Gravitational force Earth-object called? Amit gold poles to equator: friend agree weight?
Answer: Weight. No; g_poles > g_equator (smaller R, no bulge), so heavier at poles. Same mass, but weight varies slightly; friend expects less at equator.
Q10. Why paper fall slower than crumpled?
Answer: Flat paper larger area, more air resistance (friction opposes motion). Crumpled smaller area, less drag; approximates free fall. Vacuum: equal.
Q11. Moon g=1/6 Earth: 10kg weight Moon/Earth?
Answer: Earth: 98N (g=9.8). Moon: 16.33N (g=1.63). W=mg; scales with g.
Q12. Ball upward 49m/s: max height, total time return?
Answer: Height: v²=u²-2gs=0, s= (49)²/(2×9.8)=122.5m. Time up= u/g=5s, total=10s (symmetric).
Q13. Stone from 19.6m tower: final velocity ground?
Answer: v²=0+2gs=2×9.8×19.6=384.16, v=19.6 m/s.
Q14. Stone upward 40m/s, g=10: max height, displacement, distance?
Answer: Height: (40)²/(2×10)=80m. Displacement=0 (return), distance=160m (up+down).
Q15. Earth-Sun force: M_e=6×10^{24}, M_s=2×10^{30}, d=1.5×10^{11}m.
Answer: F= G M_s M_e / d² ≈3.52×10^{22}N. Keeps Earth orbit.
Q16. Stone fall 100m tower, another up 25m/s: meet when/where?
Answer: t=2s (s1=(1/2)gt²=20m down; s2=25t-(1/2)gt²=30m up; meet 20m from top). Relative motion solves.
Q17. Ball up returns 6s: velocity, max height, position 4s.
Answer: u= gt/2=29.4 m/s. Height=(u²)/(2g)=44.1m. At 4s: s= u t - (1/2) g t²=58.8-80= -21.2m (below start).
Q18. Direction buoyant force immersed object?
Answer: Upward, opposite weight; equals displaced fluid weight (Archimedes). Magnitude depends immersion/ density.
Q19. Why plastic block under water to surface?
Answer: Density < water; upthrust > weight, net upward force. Released, accelerates up until surface.
Q20. 50g substance 20cm³, water density 1g/cm³: float/sink?
Answer: Density=50/20=2.5 >1, sinks. Upthrust=20g <50g weight.
Interactive Knowledge Quiz
Test your understanding of Gravitation
Quick Revision Notes
Gravitation
- \[ F = G \frac{Mm}{d^2} \]
- g = 9.8 m/s²
- W = mg
Free Fall
- All same rate vacuum
- Equations: v=gt, s=½gt²
Buoyancy
- Upthrust = displaced weight
- Float if density < fluid
Exam Strategy Tips
- Derive formulas
- Calculate g, W
- Explain buoyancy
- Air resistance effects
- Moon weight ratio
Group Discussions
No forum posts available.
Easily Share with Your Tribe
