Gravitation Questions and Answers Class 9

NCERT Solutions for Class 9 Science Chapter 9 Gravitation Questions and Answers

Q1. State the universal law of gravitation.

Ans. According to the universal law of gravitation, every body in the universe attracts every other body with a force which is directly proportional to product of their masses and inversely proportional to the square of the distance between them. This force acts along the line joining the centres of the two bodies.

Q2. Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.

Ans. Suppose the earth is a sphere of mass Mand radius R. If an object of mass m is placed on the surface of the earth, then the magnitude of the gravitational force between the body and the earth will be:

Q1. What do you mean by free fall?

Ans. The motion of a body under the influence of force of gravity alone is called a free fall.

Q2. What do you mean by acceleration due to gravity?

Ans. The acceleration produced in the motion of a body falling under the influence of gravitational attraction to the earth is called acceleration due to gravity.

Q1. What are the differences between the mass of an object and its weight?

Ans. Differences between the mass of an object and its weight:

Mass:

1. Mass is a measure of the amount of matter contained in an object.

2. It is an intrinsic property and remains constant regardless of an object’s location.

3. Mass is measured in units such as kilograms (kg).

4. Mass determines an object’s inertia, i.e., its resistance to changes in motion.

5. In the absence of external forces, an object’s mass remains unchanged.

Weight:

1. Weight is the force exerted on an object due to gravity.

2. It depends on an object’s mass and the acceleration due to gravity.

3. Weight is a vector quantity with magnitude and direction, while mass is a scalar quantity.

4. Weight can vary depending on an object’s location in the universe.

5. Weight is measured in units such as newtons (N) or pounds (lb).

Q2. Why is the weight of an object on the moon 1/6 th its weight on the earth?

Ans. The mass of the moon of 1/100 times and its radius ¼ times that of the earth. As a result, the gravitational attraction on the moon is about one sixth of that on the earth. Hence, the weight of an object on the moon is 1/6 th of the weight on the earth.

Q1. Why is it difficult to hold a school bag having a strap made of a thin and strong string?

Ans. It is difficult to hold a school bag with a strap made of a thin and strong string because the thin string concentrates the force on a smaller area of the hand, leading to discomfort and increased pressure. The lack of width spreads the load unequally, making it harder to grip and carry comfortably.

Q2. What do you mean by buoyancy?

Ans. The upward force acting on a body immersed in a fluid is called upthrust or force of buoyancy and the phenomenon is called buoyancy.

Q3. When does an object float or sink when placed on the surface of water?

Ans. (i) An object will sink in water when its density is greater than that of water.

(ii) Conversely, an object will float on water when its density is less than that of water.

Q1. You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?

Ans. More than 42 kg. The weighing machine reads slightly less value due to the upthrust of air acting on our body.

Q2. You have a bag of cotton and an iron bar, each indicating a mass of 100 kg when measured on a weighing machine. In reality one is heavier than other. Can you say which one is heavier and why?

Ans. The cotton bag appears to be heavier than the iron bar on the weighing machine because the cotton bag experiences a greater upthrust of air compared to the iron bar. This increased upthrust causes the weighing machine to display a smaller mass for the cotton bag than its actual mass.

Exercise

Q1. How does the force of gravitation between two objects change when the distance between them is reduced to half?

Ans. According to the law of gravitation, the force of attraction between two bodies is: 

Thus the gravitational force  becomes four times the original force.

Q2. Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?

Ans. If F be the gravitational force on a body of mass m, then

Clearly, F ∝ m but g does not depend on m. Hence, all bodies fall with the same rapidness when there is no air resistance.

Q3. What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 x 10²⁴ kg and radius of the earth is 6.4 x 10⁶ m.

Ans. Here, Mass of the body (m) = 1 kg

Mass of the earth (M) = 6 x 10²⁴ kg

Radius of the earth (A)= 6.4 x 10⁶ m

Magnitude of the gravitational force between the earth and 1 kg body,

⇒ 9.77N⇒ ≈ 9.8N

Q4. 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?

Ans.

The Earth and the Moon are indeed attracted to each other by gravitational force. According to Newton’s law of universal gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Where,

r = distance between the earth and moon.

m₁ and m₂ = masses of earth and moon respectively.

The Earth is significantly more massive than the Moon, with a mass approximately 81 times greater. However, the distance between the Earth and the Moon remains relatively constant, as they both orbit around their common center of mass. As a result, the force with which the Moon attracts the Earth is the same as the force with which the Earth attracts the Moon.

This principle is known as Newton’s third law of motion, which states that for every action, there is an equal and opposite reaction. In the context of gravitational forces, the force exerted by one object on another is always accompanied by an equal and opposite force exerted by the second object on the first.

Therefore, the Earth and the Moon attract each other with an equal amount of gravitational force, despite the Earth’s greater mass.

Q5. If the moon attracts the earth, why does the earth not move towards the moon?

Ans.

According to the universal law of gravitation and Newton’s third law, the Earth and the Moon attract each other with equal but opposite forces. Despite the Earth’s larger mass, the force of attraction it exerts on the Moon is the same as the force the Moon exerts on the Earth. However, because of its greater mass, the Earth experiences a smaller acceleration towards the Moon compared to the Moon’s acceleration towards the Earth. Consequently, the Earth remains stationary, while the Moon orbits around it, resulting in the Moon’s apparent motion around our planet.

Q.6. 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?

Ans.

Q7. What is the importance of universal law of gravitation?

Ans. Importance of the universal law of gravitation: The universal law of gravitation successfully explained many phenomena occurring in nature. Some of these phenomena are as follows:

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 due to the moon and the sun.

Q8. What is the acceleration of free fall?

Ans. The acceleration experienced by an object falling solely under the influence of Earth’s gravitational force is known as gravitational acceleration. In the vicinity of Earth’s surface, this acceleration is approximately 9.8 meters per second squared (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 weight of the object.

Q10. Amit buys few grains of gold at poles as per the instruction of one of his friends. He hands over the same when he meets him at the equator. Will the friend agree with the weight of gold bought? If not, why?

[Hint: The value of g is greater at the poles than at the equator.]

Ans. No. The value of g at the equator is less than that at the poles. Hence, the few gm of gold at poles will measure less when taken to the equator.

Q11. Why will a sheet of paper fall slower than one that is crumpled into a ball?

Ans. A sheet of paper falls slower than a crumpled ball of paper due to the difference in air resistance. When a sheet of paper is flat, it presents a larger surface area to the surrounding air, which increases the amount of air resistance it experiences as it falls. This air resistance acts as a force that opposes the motion of the falling object, slowing it down.

On the other hand, when a sheet of paper is crumpled into a ball, its surface area decreases significantly. The crumpled ball presents a smaller surface area to the air, resulting in less air resistance compared to the flat sheet. With less air resistance, the crumpled ball of paper can fall more quickly because there is less force opposing its motion.

Therefore, the difference in air resistance between a flat sheet of paper and a crumpled ball affects the rate at which they fall, with the crumpled ball falling faster due to reduced air resistance.

Q12. Gravitational force on the surface of the moon is only 1/6 as strong as gravitational force on the earth. What is the weight in newtons of a 10 kg object on the moon and on the earth?

Ans. Mass of the object on the moon = 6 kg. 

Mass of the object on the earth = 6 kg. 

Weight of the object on the earth = mg = 10 x 9.8 = 98 N

 Weight of the object on the moon = 1/6 x 98 = 16.3 N

Q13. 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.

Ans. (i) In Cartesian sign convention, upward velocity is taken positive and acceleration due to gravity is taken negative.

u = +49m/s, g = – 9.8ms^-2

At the highest point, v = 0

As, v²-u²=2as

⇒ 0² – 49²= 2x(-9.8)s

Q.14. A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity just before touching the ground.

Ans. Here,

u = 40m/s, g = 9.8m/s², s = – 19.6m

As,   v²-u²=2gs

⇒ v²-0²=2x(-9.8)x(-19.6)

⇒ v² =(-19.6) x (-19.6)

⇒ v = -19.6 m/s

The negative sign indicates that the velocity is in the downward direction.

Q15. 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?

Ans. Here, Initial velocity u = 40m/s, g = 10 m/s²

Max height final velocity v = 0

Consider third equation of motion

⇒  v² = u² – 2gs [negative as the object goes up]

⇒ 0 = (40)² – 2 x 10 x s

⇒ s = (40 x 40) / 20

Maximum height h = 80m

Total Distance = h + h = 80 + 80

Total Distance = 160m

Net displacement = 80-80 = 0. (The first point is the same as the last point)

Q16. Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 × 10²⁴ kg and of the Sun = 2 × 10³⁰ kg. The average distance between the two is 1.5 × 10¹¹ m.

Ans.

Mass of the sun (m_s) = 2 × 10³⁰ kg

Mass of the earth (m_e) = 6 × 10²⁴ kg

Gravitation constant G = 6.67 x 10^-11 N m²/ kg²

Average distance r = 1.5 × 10¹¹ m

Consider Universal law of Gravitation

Q17. 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.

Ans.

(i) When the stone from the top of the tower is thrown,

Initial velocity (u) = 0

Distance travelled = x

Time taken = t

Therefore,

(ii) When the stone is thrown upwards,

Initial velocity (u) = 25 m/s

Distance travelled = (100 – x)

Time taken = t

From equations (i) and (ii)

⇒ 5t² = 100 -25t + 5t²

⇒ t = (100/25) = 4sec.

After 4sec, two stones will meet

From (a)

⇒ x = 5t² = 5 x 4 x 4 = 80m.

Putting the value of x in (100-x)

⇒ (100-80) = 20m.

This means that after 4s, 2 stones meet a distance of 20 m from the ground.

Q18. 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, and

(c) Its position after 4s.

Ans.

It is given that:

g = 10m/s²

Total time T = 6sec

Time ascent (T_a) = Time of descent (T_d) = 6/2 = 3sec

(a) Final velocity at maximum height v = 0, t = 3s, g = -9.8ms^-2

From first equation of motion:-

⇒ v = u – gt_a

⇒ u = v + gt_a

⇒ 0 + 9.8 x 3

⇒ 29.4m/s

The velocity with which stone was thrown up is 30m/s.

(b) the height,

The maximum height stone reaches is 45m.

(c) The position of the ball after 4s is given by,

The ball is at a height of 39.2m from the ground or 4.9m from the top.

Q19. In what direction does the buoyant force on an object immersed in a liquid act?

Ans: The center of buoyancy, also known as the point of application of the buoyant force, exerts an upward force on an object. This force acts vertically and is directed towards the center of gravity of the fluid that has been displaced by the object.

Q20. Why a block of plastic when released under water come up to the surface of water?

Ans: Due to its lower density compared to water, a plastic block experiences a greater buoyant force than its own weight. As a result, the plastic block undergoes an upward acceleration, causing it to rise to the surface of the water.

Q21. 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?

Ans:

To find the Density of the substance the formula is

Mass of substance = 50g

Volume of substance = 20cm³

Density = (Mass/Volume) = (50/20) = 2.5g/cm³

Density of water = 1g/cm³

Density of the substance is greater than density of water. So the substance will sink.

Q22. 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?

Ans: Mass of packet = 500 g

Volume of packet = 350cm³

Density of sealed packet = Mass/Volume = 500/350 = 1.42 g/cm³

Density of sealed packet is greater than density of water

Therefore the packet will sink.

Considering Archimedes Principle,

Displaced water volume = Force exerted on the sealed packet.

Volume of water displaced = 350cm³

Therefore displaced water mass = ρ x V

= 1 × 350

Mass of displaced water = 350g.