Gravitation Notes: Class 9 Science

Notes: Gravitation : JKBOSE Class 9 Science – Chapter 4

1. WHAT IS GRAVITATION?

ENGLISH
 Gravitation is the force of attraction between objects. It explains why objects fall toward Earth, why the Moon moves around Earth and why planets move around the Sun.

HINGLISH
 Gravitation objects ke beech attraction force hai. Isi ki wajah se objects Earth ki taraf fall karti hain, Moon Earth ke around aur planets Sun ke around move karte hain.

Gravity Explained: From Ball to Orbit

2. NEWTON’S IDEA OF GRAVITATION

ENGLISH
 Newton wondered: If Earth can attract an apple, can Earth also attract the Moon? He concluded that the same type of gravitational force acts in both cases.

HINGLISH
 Newton ne socha: Agar Earth apple ko attract kar sakti hai, toh kya Earth Moon ko bhi attract karti hai? Unhone conclude kiya ki dono cases mein gravitational force responsible hai.

Gravity Connects Apple and Moon

 

3. CENTRIPETAL FORCE

ENGLISH
 A stone tied to a thread and moved in a circle continuously changes direction. The force acting toward the centre and keeping it in circular motion is called centripetal force. If the thread is released, the stone moves along a tangent.

HINGLISH
 Thread se tied stone ko circle mein ghumane par direction continuously change hoti hai. Centre ki taraf act karne wali force ko centripetal force kehte hain. Thread release karne par stone tangent ki straight line mein move karta hai.

Centripetal Force Educational Diagram

4. UNIVERSAL LAW OF GRAVITATION

ENGLISH
 Every object in the universe attracts every other object. The force increases with mass, decreases with distance, and acts along the line joining the centres.

HINGLISH
 Universe ki har object doosri object ko attract karti hai. Mass badhne par force increase hoti hai, distance badhne par decrease hoti hai, aur force centres ko join karne wali line ke along act karti hai.

Universal Law of Gravitation Diagram

5. EFFECT OF MASS

ENGLISH
 F ∝ M × m. More mass means more gravitational force. If one mass is doubled, force becomes 2 times; if both masses are doubled, force becomes 4 times.

HINGLISH
 Mass badhega toh gravitational force badhegi. Ek mass double karne par force 2 times aur dono masses double karne par force 4 times ho jaati hai.

Edit Clear comparison infographic demonstrates how gravitational force changes when one or both masses are doubled. You could try: Refine sphere sizes and force-arrow proportions Convert it into a black-and-white exam diagram Add it to a mass-effect revision sheet Gravity: How Mass Changes Force

6. EFFECT OF DISTANCE

ENGLISH
 F ∝ 1/d². If distance becomes 2 times, force becomes 1/4; 3 times → 1/9; 6 times → 1/36. If distance becomes half, force becomes 4 times.

HINGLISH
 Distance badhne par gravitational force rapidly decrease hoti hai. 2 times distance → 1/4 force; 3 times → 1/9; 6 times → 1/36. Distance half → force 4 times.

Distance and Gravity Infographic

7. IMPORTANCE OF GRAVITATION

ENGLISH
 The law of gravitation explains why we remain attached to Earth, the Moon’s motion around Earth, planets’ motion around the Sun and tides caused by the Moon and Sun.

HINGLISH
 Gravitation explain karta hai ki hum Earth par kyun rehte hain, Moon Earth ke around kyun move karta hai, planets Sun ke around kyun move karte hain aur tides kyun aati hain.

Edit Clean Class 9 Gravitation diagram showing falling objects and orbital motion. You could try: Refine arrows and labels for textbook accuracy Convert into a handwritten Hinglish study diagram Create a printable A4 worksheet version Edit Class 9 illustration connects Newton’s apple observation with Moon’s orbital motion through gravitation. You could try: Refine Newton’s illustration and gravitational-force arrows Convert this into a Hinglish handwritten diagram Use it as a Gravitation concept-note page Edit Clear Class 9 diagram explains centripetal force and tangential motion after releasing the stone. You could try: Add velocity and tangent labels with clearer arrows Convert it into a Hinglish handwritten classroom diagram Use it in your Class 9 Gravitation notes Edit Clean textbook-style diagram shows two masses, mutual gravitational forces, distance, and Newton’s universal gravitation formula. You could try: Refine the force arrows and distance marker Create a professional black-and-white exam diagram Add this to your Class 9 Gravitation chapter notes Edit Clear comparison infographic demonstrates how gravitational force changes when one or both masses are doubled. You could try: Refine sphere sizes and force-arrow proportions Convert it into a black-and-white exam diagram Add it to a mass-effect revision sheet Create a Class 9 Physics infographic titled “EFFECT OF DISTANCE ON GRAVITATIONAL FORCE”. Show two objects at distances d, 2d and 3d with force labels F, F/4 and F/9. Add “F ∝ 1/d²”. White background, clear textbook style. Edit Clear textbook infographic shows gravitational force decreasing as distance increases from d to 3d. You could try: Refine distance markers and force labels Convert it into a clean exam-style diagram Use it for Class 9 formula revision Create a Class 9 mind map titled “IMPORTANCE OF GRAVITATION” with four branches: Earth attachment, Moon orbit, Planetary motion and Tides. Use simple Earth, Moon, Sun and ocean icons. White background. Edit Colorful Class 9 mind map explains four major applications of gravitation with clear icons and branches. You could try: Refine the four branches for visual balance Convert it into a clean textbook infographic Add it to your Gravitation chapter summary The Importance of Gravitation Infographic

8. FREE FALL

ENGLISH
 When an object falls toward Earth under the influence of gravitational force alone, it is called free fall.

HINGLISH
 Jab object sirf gravitational force ki wajah se Earth ki taraf fall karti hai, use free fall kehte hain.

Free Fall Motion Explained

9. ACCELERATION DUE TO GRAVITY

ENGLISH
 The acceleration produced by Earth’s gravitational force is called acceleration due to gravity. It is represented by g. Near Earth, g = 9.8 m/s²; for simple calculations, g = 10 m/s² may be used.

HINGLISH
 Earth ki gravitational force ki wajah se jo acceleration produce hota hai use acceleration due to gravity kehte hain. Symbol g hai. Earth ke near g = 9.8 m/s²; simple numericals mein 10 m/s² liya ja sakta hai.

Acceleration Due to Gravity Infographic

10. VALUE OF g

ENGLISH
 g = GM/R², where G is the universal gravitational constant, M is Earth’s mass and R is Earth’s radius. Near Earth, g = 9.8 m/s².

HINGLISH
 g = GM/R². G universal gravitational constant hai, M Earth ka mass aur R Earth ka radius hai. Earth ke near g = 9.8 m/s².

Gravity on Earth: Formula and Diagram

11. AIR RESISTANCE — PAPER VS STONE

ENGLISH
 A paper sheet falls slower than a stone because air resistance affects the paper more. If air is removed, both fall at the same rate.

HINGLISH
 Paper stone se slowly fall karta hai because air resistance paper ko zyada affect karti hai. Air remove karne par paper aur stone same rate se fall karenge.

Paper and Stone: Air Resistance

12. EQUATIONS OF MOTION UNDER GRAVITY

ENGLISH
 Near Earth, g is approximately constant. Therefore:

  • v = u + gt;
  • s = ut + ½gt²;
  • v² = u² + 2gs.

Here u is initial velocity, v final velocity, s displacement and t time.

HINGLISH
 Earth ke near g approximately constant hota hai, isliye a ki jagah g use karte hain:

  • v = u + gt;
  • s = ut + ½gt²;
  • v² = u² + 2gs.

Equations of Motion Under Gravity

13. OBJECT THROWN VERTICALLY UPWARD

ENGLISH
 When an object is thrown upward, gravity acts downward and slows it. At the highest point, final velocity v = 0. The object then falls back.

HINGLISH
 Object upward throw karne par gravity downward act karti hai aur speed decrease hoti hai. Highest point par v = 0 hota hai, phir object neeche fall karta hai.

Edit Clean Class 9 Gravitation diagram showing falling objects and orbital motion. You could try: Refine arrows and labels for textbook accuracy Convert into a handwritten Hinglish study diagram Create a printable A4 worksheet version Edit Class 9 illustration connects Newton’s apple observation with Moon’s orbital motion through gravitation. You could try: Refine Newton’s illustration and gravitational-force arrows Convert this into a Hinglish handwritten diagram Use it as a Gravitation concept-note page Edit Clear Class 9 diagram explains centripetal force and tangential motion after releasing the stone. You could try: Add velocity and tangent labels with clearer arrows Convert it into a Hinglish handwritten classroom diagram Use it in your Class 9 Gravitation notes Edit Clean textbook-style diagram shows two masses, mutual gravitational forces, distance, and Newton’s universal gravitation formula. You could try: Refine the force arrows and distance marker Create a professional black-and-white exam diagram Add this to your Class 9 Gravitation chapter notes Edit Clear comparison infographic demonstrates how gravitational force changes when one or both masses are doubled. You could try: Refine sphere sizes and force-arrow proportions Convert it into a black-and-white exam diagram Add it to a mass-effect revision sheet Edit Clear textbook infographic shows gravitational force decreasing as distance increases from d to 3d. You could try: Refine distance markers and force labels Convert it into a clean exam-style diagram Use it for Class 9 formula revision Edit Colorful Class 9 mind map explains four major applications of gravitation with clear icons and branches. You could try: Refine the four branches for visual balance Convert it into a clean textbook infographic Add it to your Gravitation chapter summary Edit Clear textbook diagram explains free fall through starting, highest, and falling positions under gravity. You could try: Refine the trajectory and gravity arrows Create a monochrome board-exam diagram Add this to your Class 9 notes Edit Clean Class 9 diagram shows increasing velocity during free fall due to constant downward gravitational acceleration. You could try: Refine velocity arrows and position labels Convert it into a black-and-white exam diagram Add it to your acceleration revision section Edit Clean textbook diagram connects Earth’s radius and mass to surface acceleration due to gravity. You could try: Refine the radius line and surface-object placement Create a simplified black-and-white exam version Use it for Class 9 formula revision Edit Clear comparison diagram shows how air resistance affects paper and stone during falling. You could try: Refine the falling arrows and vacuum labels Convert it into a simple exam diagram Use it for your Class 9 free-fall notes Create a highly readable Class 9 Physics formula poster titled “EQUATIONS OF MOTION UNDER GRAVITY”. Display the three formulas in separate boxes and define u, v, s, t and g. White background, clean handwritten school-notes style, 16:9. Edit Highly readable formula poster presents all three equations and clearly defines every variable. You could try: Refine formula spacing and variable definitions Convert it into a clean textbook infographic Use it as a Class 9 formula revision poster Create a Class 9 Physics diagram titled “VERTICAL UPWARD MOTION”. Show a ball moving upward through three positions, with smaller upward velocity arrows and downward gravity arrows. At the highest point write “v = 0”. White background. Edit Clear textbook diagram shows upward motion, decreasing velocity, constant downward gravity, and zero velocity at the highest point. You could try: Refine velocity arrows for clearer size differences Create a black-and-white exam-ready version Add it to your vertical-motion revision notes Vertical Upward Motion Diagram

14. SIGN CONVENTION

ENGLISH
 For upward motion, a = –g because gravity is opposite to motion. If downward is taken as positive, falling motion has a = +g.

HINGLISH
 Upward motion mein gravity opposite direction mein hoti hai, isliye a = –g. Downward ko positive lene par falling motion mein a = +g.

Vertical Motion and Gravity Infographic

15. MASS

ENGLISH
 Mass is a measure of inertia. Greater mass means greater inertia. Mass remains constant on Earth, Moon and in space. SI unit is kilogram (kg).

HINGLISH
 Mass inertia ka measure hai. Zyada mass → zyada inertia. Mass Earth, Moon aur space mein same rehta hai. SI unit kg hai.

16. WEIGHT

ENGLISH
 Weight is the force with which Earth attracts an object. W = mg. SI unit is Newton (N). Weight acts vertically downward.

HINGLISH
 Weight woh force hai jisse Earth object ko attract karti hai. W = mg. SI unit Newton (N) hai. Weight downward act karta hai.

17. MASS VS WEIGHT

ENGLISH
 Mass is constant, measured in kg and related to inertia. Weight is gravitational force, measured in N, and can change with g.

HINGLISH
 Mass constant rehta hai aur kg mein measure hota hai. Weight gravitational force hai, N mein measure hota hai aur g ke saath change ho sakta hai.

Edit Clean Class 9 Gravitation diagram showing falling objects and orbital motion. You could try: Refine arrows and labels for textbook accuracy Convert into a handwritten Hinglish study diagram Create a printable A4 worksheet version Edit Class 9 illustration connects Newton’s apple observation with Moon’s orbital motion through gravitation. You could try: Refine Newton’s illustration and gravitational-force arrows Convert this into a Hinglish handwritten diagram Use it as a Gravitation concept-note page Edit Clear Class 9 diagram explains centripetal force and tangential motion after releasing the stone. You could try: Add velocity and tangent labels with clearer arrows Convert it into a Hinglish handwritten classroom diagram Use it in your Class 9 Gravitation notes Edit Clean textbook-style diagram shows two masses, mutual gravitational forces, distance, and Newton’s universal gravitation formula. You could try: Refine the force arrows and distance marker Create a professional black-and-white exam diagram Add this to your Class 9 Gravitation chapter notes Edit Clear comparison infographic demonstrates how gravitational force changes when one or both masses are doubled. You could try: Refine sphere sizes and force-arrow proportions Convert it into a black-and-white exam diagram Add it to a mass-effect revision sheet Edit Clear textbook infographic shows gravitational force decreasing as distance increases from d to 3d. You could try: Refine distance markers and force labels Convert it into a clean exam-style diagram Use it for Class 9 formula revision Edit Colorful Class 9 mind map explains four major applications of gravitation with clear icons and branches. You could try: Refine the four branches for visual balance Convert it into a clean textbook infographic Add it to your Gravitation chapter summary Edit Clear textbook diagram explains free fall through starting, highest, and falling positions under gravity. You could try: Refine the trajectory and gravity arrows Create a monochrome board-exam diagram Add this to your Class 9 notes Edit Clean Class 9 diagram shows increasing velocity during free fall due to constant downward gravitational acceleration. You could try: Refine velocity arrows and position labels Convert it into a black-and-white exam diagram Add it to your acceleration revision section Edit Clean textbook diagram connects Earth’s radius and mass to surface acceleration due to gravity. You could try: Refine the radius line and surface-object placement Create a simplified black-and-white exam version Use it for Class 9 formula revision Edit Clear comparison diagram shows how air resistance affects paper and stone during falling. You could try: Refine the falling arrows and vacuum labels Convert it into a simple exam diagram Use it for your Class 9 free-fall notes Edit Highly readable formula poster presents all three equations and clearly defines every variable. You could try: Refine formula spacing and variable definitions Convert it into a clean textbook infographic Use it as a Class 9 formula revision poster Edit Clear textbook diagram shows upward motion, decreasing velocity, constant downward gravity, and zero velocity at the highest point. You could try: Refine velocity arrows for clearer size differences Create a black-and-white exam-ready version Add it to your vertical-motion revision notes Create a Class 9 direction diagram showing two cases: upward motion with a = –g and downward motion with a = +g when downward is positive. Clearly show motion and gravity arrows. White background. Edit Clear Class 9 direction diagram compares upward and downward motion using the downward-positive sign convention. You could try: Refine sign conventions and velocity arrows Create a simpler black-and-white exam version Add it to your equations-of-motion notes Create a Class 9 comparison infographic titled “MASS vs WEIGHT”. Left: Mass — constant, kg, inertia. Right: Weight — changes with location, N, W = mg, depends on g. Include Earth and Moon. White background. Edit Clear Class 9 comparison infographic contrasts mass and weight, including units, formulas, inertia, Earth, and Moon. You could try: Refine the Earth–Moon weight comparison Create a clean textbook line-art version Use it as a quick revision poster Mass vs Weight: Science Comparison Chart

18. WEIGHT ON THE MOON

ENGLISH
 The Moon has weaker gravity than Earth. An object’s weight on the Moon is approximately 1/6 of its Earth weight. Wmoon = Wearth/6. Example: 60 N on Earth → 10 N on Moon.

HINGLISH
 Moon ki gravity Earth se weak hai. Object ka Moon par weight approximately Earth weight ka 1/6 hota hai. Wmoon = Wearth/6. 60 N → 10 N.

Create a Class 9 comparison titled “WEIGHT ON EARTH vs MOON”. Show the same object with 60 N on Earth and 10 N on Moon. Add Wmoon = Wearth/6 and “Mass remains the same”. White background.

19. g CHANGES FROM PLACE TO PLACE

ENGLISH
 g is greater at the poles, smaller at the equator and decreases with altitude. Therefore, weight can change from place to place.

HINGLISH
 g poles par greater, equator par smaller hota hai aur altitude badhne par decrease hota hai. Isliye weight place ke saath change ho sakta hai.

Edit Clean Class 9 Gravitation diagram showing falling objects and orbital motion. You could try: Refine arrows and labels for textbook accuracy Convert into a handwritten Hinglish study diagram Create a printable A4 worksheet version Edit Class 9 illustration connects Newton’s apple observation with Moon’s orbital motion through gravitation. You could try: Refine Newton’s illustration and gravitational-force arrows Convert this into a Hinglish handwritten diagram Use it as a Gravitation concept-note page Edit Clear Class 9 diagram explains centripetal force and tangential motion after releasing the stone. You could try: Add velocity and tangent labels with clearer arrows Convert it into a Hinglish handwritten classroom diagram Use it in your Class 9 Gravitation notes Edit Clean textbook-style diagram shows two masses, mutual gravitational forces, distance, and Newton’s universal gravitation formula. You could try: Refine the force arrows and distance marker Create a professional black-and-white exam diagram Add this to your Class 9 Gravitation chapter notes Edit Clear comparison infographic demonstrates how gravitational force changes when one or both masses are doubled. You could try: Refine sphere sizes and force-arrow proportions Convert it into a black-and-white exam diagram Add it to a mass-effect revision sheet Edit Clear textbook infographic shows gravitational force decreasing as distance increases from d to 3d. You could try: Refine distance markers and force labels Convert it into a clean exam-style diagram Use it for Class 9 formula revision Edit Colorful Class 9 mind map explains four major applications of gravitation with clear icons and branches. You could try: Refine the four branches for visual balance Convert it into a clean textbook infographic Add it to your Gravitation chapter summary Edit Clear textbook diagram explains free fall through starting, highest, and falling positions under gravity. You could try: Refine the trajectory and gravity arrows Create a monochrome board-exam diagram Add this to your Class 9 notes Edit Clean Class 9 diagram shows increasing velocity during free fall due to constant downward gravitational acceleration. You could try: Refine velocity arrows and position labels Convert it into a black-and-white exam diagram Add it to your acceleration revision section Edit Clean textbook diagram connects Earth’s radius and mass to surface acceleration due to gravity. You could try: Refine the radius line and surface-object placement Create a simplified black-and-white exam version Use it for Class 9 formula revision Edit Clear comparison diagram shows how air resistance affects paper and stone during falling. You could try: Refine the falling arrows and vacuum labels Convert it into a simple exam diagram Use it for your Class 9 free-fall notes Edit Highly readable formula poster presents all three equations and clearly defines every variable. You could try: Refine formula spacing and variable definitions Convert it into a clean textbook infographic Use it as a Class 9 formula revision poster Edit Clear textbook diagram shows upward motion, decreasing velocity, constant downward gravity, and zero velocity at the highest point. You could try: Refine velocity arrows for clearer size differences Create a black-and-white exam-ready version Add it to your vertical-motion revision notes Edit Clear Class 9 direction diagram compares upward and downward motion using the downward-positive sign convention. You could try: Refine sign conventions and velocity arrows Create a simpler black-and-white exam version Add it to your equations-of-motion notes Edit Clear Class 9 comparison infographic contrasts mass and weight, including units, formulas, inertia, Earth, and Moon. You could try: Refine the Earth–Moon weight comparison Create a clean textbook line-art version Use it as a quick revision poster Create a Class 9 comparison titled “WEIGHT ON EARTH vs MOON”. Show the same object with 60 N on Earth and 10 N on Moon. Add Wmoon = Wearth/6 and “Mass remains the same”. White background. Edit Clear Class 9 infographic compares the same object’s weight on Earth and Moon using 60 N and 10 N. You could try: Refine the weight relationship and gravity labels Create a clean textbook line-art version Use it for a mass-and-weight revision poster Create a Class 9 diagram titled “g CHANGES WITH LOCATION”. Show Earth with poles and equator, label “g greater at poles”, “g smaller at equator”, and show altitude increasing with “g decreases”. White background. Edit Clear Class 9 diagram shows how gravitational acceleration varies between poles, equator, and increasing altitude. You could try: Refine the altitude sequence and g labels Create a clean black-and-white exam diagram Use it for Class 9 concept revision Gravity Changes Across Earth and Altitude

Gravitation Important Formulas Study Sheet

🧠 COMPLETE CHAPTER MIND MAP

GRAVITATION → Universal Law → Free Fall → Acceleration due to Gravity → Equations of Motion → Mass → Weight → Moon → Buoyancy → Density → Float/Sink

Gravitation: A Colorful Science Mind Map

CHAPTER 4 — GRAVITATION EXERCISE QUESTIONS — COMPLETE ANSWERS

Question: How does the force of gravitation between two objects change when the distance between them is reduced to half?

Answer: According to the universal law of gravitation:

F ∝ 1/d²

If the distance becomes half:

d′ = d/2

Therefore:

F′ = GMm/(d/2)²
F′ = 4GMm/d²

So,  F′ = 4F

Therefore, the gravitational force becomes 4 times the original force.

Question: Gravitational force acts on all objects in proportion to their masses. Why then, does a heavy object not fall faster than a light object?

Answer: The acceleration due to gravity is independent of the mass of the falling object.

For a freely falling object:

F = mg

Also:   F = ma

Therefore:  ma = mg
a = g

Thus, in the absence of air resistance, all objects fall with the same acceleration due to gravity, irrespective of their masses.

Question: What is the magnitude of the gravitational force between the Earth and a 1 kg object on its surface?

Answer: Given:

Mass of Earth, M = 6 × 10²⁴ kg
Mass of object, m = 1 kg
Radius of Earth, R = 6.4 × 10⁶ m
G = 6.7 × 10⁻¹¹ N m² kg⁻²

Using:

F = GMm/R²

F = (6.7 × 10⁻¹¹ × 6 × 10²⁴ × 1)/(6.4 × 10⁶)²

F ≈ 9.8 N

Therefore, the gravitational force is approximately 9.8 N.

Question: The Earth and the Moon are attracted to each other by gravitational force. Does the Earth attract the Moon with a force that is greater or smaller or the same as the force with which the Moon attracts the Earth? Why?

Answer: The Earth and Moon attract each other with equal gravitational forces.

According to Newton’s third law of motion, every action has an equal and opposite reaction.

Therefore:

Force of Earth on Moon = Force of Moon on Earth

The forces are equal in magnitude but opposite in direction.

Question: If the Moon attracts the Earth, why does the Earth not move towards the Moon?

Answer: The Moon and Earth attract each other with equal force.  However, the mass of Earth is much greater than the mass of the Moon.

From:

F = ma

For the same force, acceleration is smaller when mass is larger. Therefore, the acceleration of Earth is extremely small compared with that of the Moon.  Hence, the movement of Earth towards the Moon is not noticeable.

Question: What happens to the force between two objects if:

(i) the mass of one object is doubled?

(ii) the distance between the objects is doubled and tripled?

(iii) the masses of both objects are doubled?

Answer: Using:

F = Gm₁m₂/d²

(i) If one mass is doubled:  Force becomes 2 times.

(ii) If distance is doubled: Force becomes 1/4 times.

If distance is tripled: Force becomes 1/9 times.

(iii) If both masses are doubled:  The product of masses becomes 4 times.

Therefore, force becomes 4 times.

Question: What is the importance of the universal law of gravitation?

Answer: The universal law of gravitation explains:

1. The force that binds us to the Earth.
2. The motion of the Moon around the Earth.
3. The motion of planets around the Sun.
4. The tides caused by the Moon and the Sun.

Question: What is the acceleration of free fall?

Answer: The acceleration produced in an object due to the gravitational force of Earth is called acceleration due to gravity.

It is represented by g.  Near the surface of Earth:

g = 9.8 m/s².

Question: What do we call the gravitational force between the Earth and an object?

Answer: The gravitational force with which Earth attracts an object is called the weight of the object.

W = mg

The SI unit of weight is newton (N).

Question: Amit buys a few grams of gold at the poles as instructed by his friend. He hands over the same gold when he meets his friend at the equator. Will the friend agree with the weight of the gold bought? If not, why?

Answer: No, the friend will not agree with the weight.

The mass of the gold remains the same, but the value of g is greater at the poles than at the equator.

Since:  W = mg

the weight of the gold is greater at the poles and slightly smaller at the equator.

Therefore, the gold has slightly less weight at the equator.

Question: Why will a sheet of paper fall slower than one that is crumpled into a ball?

Answer: A flat sheet of paper has a larger surface area and therefore experiences more air resistance.  A crumpled paper ball has a smaller surface area and experiences less air resistance. Therefore, the crumpled paper falls faster.

If air resistance is removed, both would fall at the same rate.

Question: Gravitational force on the surface of the Moon is only 1/6 as strong as gravitational force on Earth. What is the weight in newtons of a 10 kg object on the Moon and on Earth?

Answer: Given:

Mass = 10 kg
g on Earth = 9.8 m/s²

Weight on Earth:

W = mg
W = 10 × 9.8
W = 98 N

Weight on Moon:

Wmoon = Wearth/6
Wmoon = 98/6
Wmoon ≈ 16.3 N

Therefore:  Weight on Earth = 98 N and  Weight on Moon ≈ 16.3 N.

Question: A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate: (i) the maximum height to which it rises (ii) the total time it takes to return to the surface of the Earth.

Answer: Given:

u = 49 m/s
v = 0 m/s at maximum height
g = 9.8 m/s²

(i) Maximum height

Using:  v² = u² − 2gh

0 = 49² − 2 × 9.8 × h

h = 122.5 m

(ii) Time to reach maximum height:

v = u − gt

0 = 49 − 9.8t

t = 5 s

Total time:  T = 2 × 5 = 10 s

Therefore:  Maximum height = 122.5 m
Total time = 10 s.

Question: A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity just before touching the ground.

Answer: Given:

u = 0 m/s
s = 19.6 m
g = 9.8 m/s²

Using:  v² = u² + 2gs

v² = 0 + 2 × 9.8 × 19.6

v² = 384.16

v = 19.6 m/s

Therefore, the final velocity is 19.6 m/s downward.

Question: A stone is thrown vertically upward with an initial velocity of 40 m/s. Taking g = 10 m/s², find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone?

Answer: Given:

u = 40 m/s
v = 0 m/s at maximum height
g = 10 m/s²

Maximum height:  v² = u² − 2gh

0 = 40² − 2 × 10 × h

h = 80 m

The stone returns to the same point from which it was thrown.

Net displacement = 0 m

Total distance:  = 80 + 80  = 160 m

Therefore: Maximum height = 80 m
Net displacement = 0 m
Total distance = 160 m.

Question: Calculate the force of gravitation between the Earth and the Sun, given that the mass of the Earth = 6 × 10²⁴ kg and the mass of the Sun = 2 × 10³⁰ kg. The average distance between the two is 1.5 × 10¹¹ m.

Answer: Given:

Mass of Earth, M = 6 × 10²⁴ kg
Mass of Sun, m = 2 × 10³⁰ kg
Distance, d = 1.5 × 10¹¹ m
G = 6.7 × 10⁻¹¹ N m² kg⁻²

Using:  F = GMm/d²

F = [(6.7 × 10⁻¹¹)(6 × 10²⁴)(2 × 10³⁰)]/(1.5 × 10¹¹)²

F ≈ 3.57 × 10²² N

Therefore, the gravitational force between Earth and Sun is approximately 3.57 × 10²² N.

Question: A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Calculate when and where the two stones will meet.

Answer: Let the stones meet after t seconds.  For the stone falling from the top:

u = 0

Distance travelled: s₁ = ½gt²

For the stone projected upward:

u = 25 m/s

Distance travelled:

s₂ = 25t − ½gt²

At the meeting point:

s₁ + s₂ = 100

½gt² + 25t − ½gt² = 100

25t = 100

t = 4 s

Distance travelled by the falling stone:

s₁ = ½ × 9.8 × 4²
s₁ = 78.4 m

Height above ground:  100 − 78.4 = 21.6 m

Therefore, the stones meet after 4 s at a height of 21.6 m above the ground.

Question: A ball thrown up vertically returns to the thrower after 6 s. Find: (a) the velocity with which it was thrown up (b) the maximum height it reaches (c) its position after 4 s.

Answer: Total time = 6 s

Time to reach maximum height:

t = 6/2 = 3 s

Take g = 9.8 m/s².

(a) Initial velocity

At maximum height, v = 0.

v = u − gt

0 = u − 9.8 × 3

u = 29.4 m/s

(b) Maximum height

h = u²/2g

h = (29.4)²/(2 × 9.8)

h = 44.1 m

(c) Position after 4 s

The ball reaches maximum height after 3 s.

After 4 s, it has been falling for:

4 − 3 = 1 s

Distance fallen in 1 s:

s = ½gt²
s = ½ × 9.8 × 1²
s = 4.9 m

Position above ground:

44.1 − 4.9 = 39.2 m

Therefore:  Initial velocity = 29.4 m/s
Maximum height = 44.1 m
Position after 4 s = 39.2 m above the ground.

Question: In what direction does the buoyant force on an object immersed in a liquid act?

Answer: The buoyant force acts in the vertically upward direction.  The liquid pushes the immersed object upward.

Question: Why does a block of plastic released under water come up to the surface of water?

Answer: Two main forces act on the plastic block:

• Gravitational force acts downward.
• Buoyant force acts upward.

The plastic block has lower density than water, so the upward buoyant force is greater than its weight.

Therefore, the block moves upward and comes to the surface of water.

Question: The volume of 50 g of a substance is 20 cm³. If the density of water is 1 g cm⁻³, will the substance float or sink?

Answer: Given:

Mass = 50 g
Volume = 20 cm³

Density = Mass/Volume

Density = 50/20
Density = 2.5 g/cm³

Density of water = 1 g/cm³.

Since the density of the substance is greater than the density of water, the substance will sink.

Answer: The substance will sink.

Question: The volume of a 500 g sealed packet is 350 cm³. Will the packet float or sink in water if the density of water is 1 g cm⁻³? What will be the mass of the water displaced by this packet?

Answer: Given:

Mass of packet = 500 g
Volume = 350 cm³

Density = Mass/Volume

Density = 500/350
Density ≈ 1.43 g/cm³

Density of water = 1 g/cm³.

Since 1.43 g/cm³ > 1 g/cm³, the packet will sink.

Volume of water displaced = 350 cm³.

Mass of displaced water:

Mass = Density × Volume
Mass = 1 × 350
Mass = 350 g

Therefore:  The packet will sink.
Mass of displaced water = 350 g.

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