Class 9 General Science Chapter 10 Gravitation
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Class 9 General Science Chapter 10 Gravitation
Answers to Questions Within the Lesson(1)
Q1. State the universal law of gravitation.
Ans: The Universal Law of Gravitation states that every two objects in the universe attract each other with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Q2. Write the formula to calculate the gravitational force between the Earth and an object on its surface.
Ans: The gravitational force between the Earth and an object is given by the formula:
F = GMm / R²
where G is the gravitational constant, M is the mass of the Earth, m is the mass of the object, and R is the radius of the Earth.
Answers to Questions Within the Lesson(2)
Q1. What is meant by free fall?
Ans: Free fall refers to the motion of an object when it falls under the influence of gravity alone, without any other external force acting on it.
Q2. What is meant by acceleration due to gravity?
Ans: Acceleration due to gravity is the acceleration produced in a body due to the gravitational force of the Earth. It is denoted by g, and its value near the Earth’s surface is approximately 9.8 m/s².
Answers to Questions Within the Lesson(3)
Q3. What are the differences between mass and weight?
Ans: Mass is the amount of matter in a body, whereas weight is the force with which the Earth attracts the body. Mass is constant everywhere, but weight changes from place to place depending on gravity. The SI unit of mass is kilogram (kg), while the SI unit of weight is newton (N). Mass is a scalar quantity, whereas weight is a vector quantity.
Q2. Why is the weight of an object on the surface of the Moon equal to1/6 of its weight on the Earth?
Ans: The weight of an object depends on gravitational acceleration. Since the Moon is much smaller than the Earth, its gravitational pull is weaker. The acceleration due to gravity on the Moon is about 1/6 of that on the Earth. Therefore, the weight of an object on the Moon becomes 1/6 of its weight on the Earth.
Answers to Questions Within the Lesson(4)
Q1. Why is it uncomfortable to carry a school bag with thin but strong straps?
Ans: It is uncomfortable because pressure depends on the area over which force is applied. Thin straps have a smaller area, so they exert greater pressure on the shoulders. This increased pressure causes discomfort while carrying the bag.
Q2. What is buoyancy?
Ans: Buoyancy is the upward force exerted by a liquid on an object when it is immersed in it.
Q3. Why does an object float or sink in water?
Ans: Whether an object floats or sinks depends on its density. If the density of the object is greater than that of water, it sinks because the upward buoyant force is less than its weight. If its density is less than that of water, it floats because the buoyant force is greater than its weight.
Answers to Questions Within the Lesson(5)
Q1. According to a weighing machine, your mass is 42 kg. Is your actual mass less or more than 42 kg?
Ans: The actual mass is slightly more than 42 kg. This is because the weighing machine measures the apparent weight, which is slightly less due to the upward buoyant force of air acting on the body.
Q2. You have a bag of cotton and an iron rod. Each shows a mass of 100 kg on a weighing machine. In reality, one feels heavier than the other. Which one is heavier and why?
Ans: The iron rod is actually heavier. The cotton bag has a larger volume and experiences a greater buoyant force from air, which reduces its apparent weight more than that of the iron rod. Hence, even though both show the same mass on the machine, the iron rod is truly heavier.
Exercise: Questions and Answers
Q1. If the distance between two objects is reduced to half of its original value, how will the gravitational force between them change?
Ans: If the distance between two objects is reduced to half, the gravitational force between them becomes four times the original value.
Q2. Gravitational force acts on objects in proportion to their masses. Then why does a heavier object not fall faster than a lighter object?
Ans: When an object falls, it experiences an acceleration that does not depend on its mass. This acceleration is due to gravity and is the same for all objects (ignoring air resistance). Therefore, both heavy and light objects fall at the same rate, even though the gravitational force acting on them is proportional to their masses.
Q3. What is the gravitational force between the Earth and a body of mass 1 kg on its surface? (Mass of Earth = 6 × 10²⁴ kg and radius of Earth= 6.4 × 106 m)
F = GMm/R²
Ans:
Given,
G = 6.67 × 10?-1¹¹ N·m²/kg²
M = 6 × 10²⁴ kg
m = 1 kg
R = 6.4 × 106 m
Substituting values:
F = (6.67 × 10-¹¹ × 6 × 10²⁴ × 1) / (6.4 × 106)²
F ≈ 9.8 N
Q4. The Earth and the Moon attract each other due to gravitational force. Is the force with which the Earth attracts the Moon equal to, less than, or greater than the force with which the Moon attracts the Earth? Why?
Ans: The forces are equal in magnitude. According to Newton’s Third Law of Motion, the Earth and the Moon exert equal and opposite gravitational forces on each other.
Q5. Even though the Moon attracts the Earth, why does the Earth not move towards the Moon?
Ans: Although the forces are equal, the Earth has a much larger mass than the Moon. Therefore, the acceleration produced in the Earth is extremely small, so its motion toward the Moon is not noticeable.
Q6. What will be the change in 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?
Ans:
(i) If one mass is doubled, the gravitational force becomes double.
(ii) If the distance is doubled, the force becomes 1/4; if tripled, it becomes1/9.
(iii) If both masses are doubled, the force becomes 4 times.
Q7. What is the importance of the universal law of gravitation?
Ans: The importance of the Universal Law of Gravitation is:
It explains the force that binds us to the Earth.
It explains the motion of the Moon around the Earth.
It explains the motion of planets around the Sun.
It explains phenomena like tides caused by the Moon and the Sun.
Q8. What is the acceleration due to free fall?
Ans: The acceleration due to free fall is 9.8 m/s².
Q9. What do we call the gravitational force between the Earth and an object?
Ans: The gravitational force between the Earth and an object is called the weight of the object.
Q10. Amit bought some gold from his friend in the polar region. When they met again at the equator, he returned the gold. Will the friend accept the same weight? If not, why? (Hint: g is greater at the poles than at the equator.)
Ans: No, he will not accept the same weight. Weight depends on gravitational acceleration. Since the value of g is greater at the poles than at the equator, the weight of the gold at the equator will be less than at the poles.
Q11. Why does a sheet of paper fall slowly compared to a crumpled paper ball?
Ans: The rate of fall depends on surface area and air resistance. A flat sheet of paper has a larger surface area, so it experiences greater air resistance and falls slowly. A crumpled paper ball has a smaller surface area, so it falls faster.
Q12. The gravitational force on the surface of the Moon is 1/6 of that on the Earth. What will be the weight (in newtons) of a body of mass 10 kg on the Moon?
Ans:
Mass, m = 10 kg
Acceleration due to gravity on Moon = g/6 ≈ 9.8/6 ≈ 1.63 m/s²
Weight on Moon = m × gₘ
= 10 × 1.63 ≈ 16.3 N
Q13. A ball is thrown vertically upward with a velocity of 49 m/s.
(i) Find the maximum height reached
(ii) Find the total time taken to return to the ground
v² = u² – 2gh
Ans:
(i) At highest point, v = 0
0 = (49)² – 2 × 9.8 × h
h = 49² / (2 × 9.8)
h = 2401 / 19.6 = 122.5 m
v = u – gt
(ii) For upward journey:
0 = 49 – 9.8t
t = 5 s
Total time = 2 × 5 = 10 s
Q14. A stone is dropped from a height of 19.6 m. Find its final velocity just before it touches the ground.
v²= u² + 2gh
Ans:
Initial velocity, u = 0
g = 9.8 m/s²
h = 19.6 m
v² = 2 × 9.8 × 19.6 = 384.16
v = 19.6 m/s
Final velocity = 19.6 m/s downward
Q15. A stone is thrown vertically upward with a velocity of 40 m/s. Taking g = 10 m/s², find the maximum height reached. Also find the total displacement and total distance travelled.
v²= u²- 2gh
Ans:
At highest point, v = 0
0 = (40)² – 2 × 10 × h
h = 1600 / 20 = 80 m
Maximum height = 80 m
Total displacement = 0 (returns to starting point)
Total distance travelled = 80 + 80 = 160 m
Q17. A stone is dropped from the top of a 100 m high tower. At the same time, another stone is thrown vertically upward with a velocity of 25m/s from the ground. When and where will the two stones meet?
Ans:
Let the stones meet after time t seconds.
Distance fallen by first stone:
s1 = (1/2)gt² = 5t²
Distance covered by second stone upward:
s1= ut – (1/2)gt² = 25t – 5t²
At meeting point:
s₁+ s₂ = 100
5t² + (25t – 5t²) = 100
25t = 100
t = 4 s
Position of meeting point from ground:
s₂ = 25(4) – 5(4)²
= 100 – 80
= 20 m
Therefore, the stones meet after 4 seconds at a height of 20 m above the ground.
Q18. A stone thrown vertically upward returns to the thrower after 6seconds.
(a) Find its initial upward velocity
(b) Find the maximum height reached
(c) Find its position after 4 seconds
Ans:
Given, total time of flight = 6 s
Time of ascent = 6 / 2 = 3 s
(a) Initial velocity:
u = g × t = 9.8 × 3 = 29.4 m/s
(b) Maximum height:
h = ut – 1/2gt²
h = (29.4 × 3) – (1/2 × 9.8 × 3²)
= 88.2 – 44.1
= 44.1 m
(c) Position after 4 s:
s = ut – (1/2)gt²
= (29.4 × 4) – (1/2 × 9.8 × 16)
= 117.6 – 78.4
= 39.2 m
So, after 4 seconds, the stone is 39.2 m above the point of projection.
Q19. In which direction does the buoyant force act on an object immersed in a liquid?
Ans: The buoyant force acts in the upward direction, opposite to the force of gravity.
Q20. Why does a piece of plastic released under water come back to the surface?
Ans: The plastic piece comes back to the surface because the buoyant force acting on it is greater than its weight. This upward force pushes it towards the surface.
Q21. An object has a mass of 50 g and a volume of 20 cm³. If the density of water is 1 g/cm³, will the object float or sink?
Ans:
Density of object = mass / volume = 50 / 20 = 2.5 g/cm³
Since the density of the object (2.5 g/cm³) is greater than the density ofwater (1 g/cm³), the object will sink in water.
Q22. A sealed packet has a mass of 500 g and a volume of 350 cm³. If the density of water is 1 g/cm³, will the packet float or sink? Also find the mass of water displaced by the packet.
Ans:
Density of packet = mass / volume = 500 / 350 ≈ 1.43 g/cm³
Since the density of the packet is greater than that of water (1 g/cm³), the packet will sink.
Mass of water displaced = volume × density of water
= 350 × 1 = 350 g
Therefore, the packet sinks and displaces 350 g of water.
Additional Questions & Answers
Q1. Define the following: mass, weight, gravitational force, centripetal force, thrust, pressure, buoyancy.
Ans:
Mass: The amount of matter contained in an object is called its mass.
Weight: The force with which an object is attracted towards the Earth is called its weight.
Gravitational force: The force of attraction between any two objects in the universe is called gravitational force.
Centripetal force: The force that acts towards the centre and keeps a body moving in a circular path is called centripetal force.
Thrust: The force acting perpendicular to the surface of an object is called thrust.
Pressure: The thrust acting per unit area is called pressure.
Buoyancy: The upward force exerted by a liquid on an immersed object is called buoyancy.
Q2. Write the SI units of the following: mass, weight, pressure, density.
Ans:
SI unit of mass: kilogram (kg)
SI unit of weight: newton (N)
SI unit of pressure: pascal (Pa) or N/m²
SI unit of density: kg/m³
Q3. State Archimedes’ principle.
Ans: According to Archimedes’ Principle, when a body is wholly or partially immersed in a liquid, it experiences an upward force equal to the weight of the liquid displaced by it.
Q4. What is relative density?
Ans: Relative density is the ratio of the density of a substance to the density of water.
Q5. Why does an iron nail sink in water while a closed bottle floats?
Ans: An iron nail sinks because its weight is greater than the buoyant force acting on it. In contrast, a closed bottle floats because the buoyant forceacting on it is greater than its weight due to the air trapped inside, which reduces its overall density.
Q6. Write some applications of Archimedes’ principle.
Ans:
It is used in designing ships and submarines.
It is used in making instruments like hydrometers and lactometers to measure the density of liquids.
Q7. What is the density of water?
Ans: The density of water is 1000 kg/m³.
Multiple Choice Questions (MCQ)
1. The force of attraction between two objects in the universe is called
(a) Magnetic force
(b) Electric force
(c) Gravitational force
(d) Nuclear force
Ans: (c)
2. According to Universal Law of Gravitation, the gravitational force between two masses is proportional to
(a) sum of masses
(b) difference of masses
(c) product of masses
(d) square of masses
Ans: (c)
3. Gravitational force is always
(a) repulsive
(b) attractive
(c) zero
(d) random
Ans: (b)
4. The SI unit of gravitational force is
(a) joule
(b) newton
(c) watt
(d) pascal
Ans: (b)
5. The value of gravitational constant (G) is approximately(a) 6.67 × 10?¹¹ N·m²/kg²
(b) 9.8 m/s²
(c) 3 × 108 m/s
(d) 1.6 × 108 m/s
Ans: (a)
6. If the distance between two bodies is doubled, the gravitational force becomes
(a) double
(b) half
(c) one-fourth
(d) four times
Ans: (c)
7. The force that keeps planets in their orbits is
(a) friction
(b) magnetic force
(c) gravitational force
(d) electric force
Ans: (c)
8. Acceleration due to gravity on Earth is approximately
(a) 10 m/s²
(b) 9.8 m/s²
(c) 8 m/s²
(d) 12 m/s²
Ans: (b)
9. The value of g on the Moon is about
(a) same as Earth
(b) double of Earth
(c) half of Earth
(d) one-sixth of Earth
Ans: (d)
10. The weight of an object depends on
(a) its mass
(b) acceleration due to gravity
(c) both mass and gravity
(d) volume
Ans: (c)
11. The SI unit of weight is
(a) kilogram
(b) gram
(c) newton
(d) metre
Ans: (c)
12. If mass of a body is doubled, its weight becomes
(a) half
(b) same
(c) double
(d) zero
Ans: (c)
13. Free fall means motion under
(a) friction only
(b) gravity only
(c) air resistance
(d) magnetic force
Ans: (b)
14. The value of g decreases
(a) at sea level
(b) at poles
(c) with increase in height
(d) at equator
Ans: (c)
15. The force between Earth and an object is called its
(a) mass
(b) density
(c) weight
(d) pressure
Ans: (c)
16. Who discovered the law of gravitation?
(a) Galileo
(b) Einstein
(c) Isaac Newton
(d) Archimedes
Ans: (c)
17. The force of gravity acts
(a) upward
(b) downward
(c) towards centre of Earth
(d) sideways
Ans: (c)
18. Weight is a
(a) scalar quantity
(b) vector quantity
(c) constant quantity
(d) zero quantity
Ans: (b)
19. Mass is a
(a) vector quantity
(b) scalar quantity
(c) force
(d) velocity
Ans: (b)
20. The value of g is maximum at
(a) equator
(b) poles
(c) centre of Earth
(d) space
Ans: (b)
21. The gravitational force between two objects depends on
(a) their masses
(b) distance between them
(c) both (a) and (b)
(d) neither
Ans: (c)
22. The unit of G is
(a) N·m²/kg²
(b) N/kg
(c) kg/m³
(d) m/s²
Ans: (a)
23. When an object is thrown upward, its velocity at highest point is(a) maximum
(b) zero
(c) infinite
(d) constant
Ans: (b)
24. If an object is in free fall, its acceleration is
(a) zero
(b) increasing
(c) constant
(d) decreasing
Ans: (c)
25. The weight of an object becomes zero
(a) on Earth
(b) on Moon
(c) in free fall
(d) in water
Ans: (c)
26. If distance between two objects is tripled, force becomes
(a) 1/3
(b) 1/9
(c) 3 times
(d) 9 times
Ans: (b)
27. Gravitational force between two objects is independent of
(a) their mass
(b) distance
(c) medium between them
(d) both (a) and (b)
Ans: (c)
28. The Earth attracts objects due to
(a) magnetic force
(b) gravitational force
(c) electric force
(d) friction
Ans: (b)
29. The time taken to reach the ground in free fall depends on
(a) mass
(b) height
(c) gravity
(d) both (b) and (c)
Ans: (d)
30. The weight of a body is minimum
(a) at poles
(b) at equator
(c) at centre of Earth
(d) at sea level
Ans: (c)
