10. Gravitation

Class 9 Science Chapter 10. Gravitation

Chapter 10. Gravitation

Class 9 Science Chapter 10. Gravitation Example / Internal Questions and Answers :

Example 10.1 : The mass of the earth is kg and that of the moon is . If the distance between the earth and the moon is km, calculate the force exerted by the earth on the moon. (Take G = )

Solution: The mass of the earth, M kg

The mass of the moon, m kg

The distance between the earth and the moon, d km

The force exerted by the earth on the moon is

Internal Questions :

1. State the universal law of gravitation.

Answer: The law of gravitation states that the force of attraction between any two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.
2. Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.

Answer: The formula of the magnitude of the gravitational force between the earth and an object on the surface of the earth is

Example 10.2 A car falls off a ledge and drops to the ground in 0.5 s. Let g = 10 (for simplifying the calculations).
(i) What is its speed on striking the ground?
(ii) What is its average speed during the 0.5 s?
(iii) How high is the ledge from the ground?

Solution: Time second

Initial velocity

Acceleration due to gravity,

Acceleration of the car, (downward)

(i) speed

m/s

(ii) Average speed

(iii) Distance travelled,

(i) Its speed on striking the ground

(ii) Its average speed during the

(iii) Height of the ledge from the ground = 1.25 m.

Example 10.3 An object is thrown vertically upwards and rises to a height of 10 m. Calculate (i) the velocity with which the object was thrown upwards and (ii) the time taken by the object to reach the highest point.

Solution: Distance travelled , Final velocity

Acceleration due to gravity,

Acceleration of the object, (upward motion)

(i)

(ii)

Thus, (i) Initial velocity, u = 14 , and

(ii) Time taken, t = 1.43 s.

Internal Questions :

1. What do you mean by free fall?

Answer: Free fall occurs when objects are solely influenced by the Earth's gravitational force, causing them to move towards the Earth. It signifies objects falling due to gravity alone.
2. What do you mean by acceleration due to gravity?

Answer: When an object falls towards the earth, an acceleration is involved. This acceleration is due to the earth’s gravitational force. This acceleration is called the acceleration due to the gravitational force of the earth or acceleration due to gravity. It is denoted by g . The value of g is 9.8 m/s² .

Example 10.4 Mass of an object is 10 kg. What is its weight on the earth?

Solution: Here, Mass, m = 10 kg

Acceleration due to gravity, g = 9.8

W = m × g

W = 10 kg × 9.8 = 98 N

Thus, the weight of the object is 98 N.

Example 10.5 An object weighs 10 N when measured on the surface of the earth. What would be its weight when measured on the surface of the moon .

Solution: We know,

Weight of object on the moon Weight on the earth.

= 1.67 N .

Thus, the weight of object on the surface of the moon would be 1.67 N.

Internal Questions :

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

Answer : The differences between the mass of an object and weight are :

Mass:

(i) The mass of an object is the measure of its inertia .

(ii) The mass stays constant.

(iii) It is measured in kilograms.

Weight:

(i) The weight of a body is the force with which the earth attracts it.

(ii) The weight may vary from place to place .

(iii) It is measured in units called newtons.

2. Why is the weight of an object on the moon its weight on the earth?

Answer: The weight of an object on the Moon is of its weight on Earth because the Moon has less gravity compared to Earth. Gravity is what pulls objects towards the ground. Since the Moon has weaker gravity, it cannot pull objects as strongly as Earth does. Therefore, objects weigh less on the Moon than on Earth.

Example 10.6 A block of wood is kept on a tabletop. The mass of wooden block is 5 kg and its dimensions are 40 cm × 20 cm × 10 cm. Find the pressure exerted by the wooden block on the table top if it is made to lie on the table top with its sides of dimensions (a) 20 cm × 10 cm and (b) 40 cm × 20 cm.

Solution: The mass of the wooden block (m) = 5 kg

The dimensions of the wooden block = 40 cm × 20 cm × 10 cm

If the weight of the wooden block applies a thrust on the table top, then

Thrust

= 49 N

Area of a side = length × breadth

Pressure

When the block lies on its side of dimensions 40 cm × 20 cm, it exerts the same thrust.

Area of the side = length × breadth

Pressure

The pressure exerted by the side 20 cm × 10 cm is 2450 and by the side 40 cm × 20 cm is 612.5 .

Internal Questions :

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

Answer: It is difficult to hold a school bag with a strap made of a thin and strong string because the thin string puts a lot of pressure on our hand or fingers. The thin string concentrates the force over a small area, making it uncomfortable to hold and causing strain or pain in our hand or fingers.
2. What do you mean by buoyancy ?

Answer: The upward force exerted by the water on the object is known as upthrust or buoyant force. All objects experience a force of buoyancy when they are immersed in a fluid. The magnitude of this buoyant force depends on the density of the fluid.
3. Why does an object float or sink when placed on the surface of water ?

Answer: An object floats or sinks when placed on the surface of water due to the balance between its weight and the buoyant force exerted by the water. If the object's weight is less than the buoyant force, it floats. If it is greater, it sinks.

Internal Questions :

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

Answer: If the weighing machine displays your mass as 42 kg, then your mass is indeed 42 kg. The weighing machine measures your mass, which is the amount of matter in your body, and it provides an accurate reading of that mass. Therefore, your mass is exactly 42 kg.
2. 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?

Answer: Given that both the bag of cotton and the iron bar indicate a mass of 100 kg on the weighing machine, we cannot determine which one is actually heavier based solely on the weighing machine reading. The weighing machine measures mass, not weight, and it is possible for two objects with different weights to have the same mass. Weight depends on the gravitational force acting on an object, while mass is the amount of matter in an object. To determine which one is heavier, we would need to compare their weights using a scale or balance in a gravitational field.

Example 10.7 Relative density of silver is 10.8. The density of water is . What is the density of silver in SI unit ?

Solution: Relative density of silver = 10.8

Relative density

Density of silver = Relative density of silver × density of water

Class 9 Science Chapter 10. Gravitation Exercise Questions and Answers :

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

Answer: We know that, the force between two objects is inversely proportional to the square of the distance between them .

For First object :

For second object :

,Where, k is the constant .

Given,

We have

The force of gravitation becomes 4 times more .
2. Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?

Answer : The gravitational force acting on objects is proportional to their masses, a heavy object does not fall faster than a light object because the mass of heavy object has more inertia and the mass of light object has low inertia . The increased inertia means the stronger gravitational force . So, a heavy object does not fall faster than a light object .
3. What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is kg and radius of the earth is m.)

Answer : Given, Mass of the object kg

Mass of the earth kg

and radius of the earth m

Using Newton's law of universal gravitation,

4. 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: According to Newton's third law of motion, the Earth attracts the Moon with the same force with which the Moon attracts the Earth. The gravitational force between two objects depends on their masses, and as long as the masses of the Earth and the Moon remain the same, the attractive forces they exert on each other are equal.
5. If the moon attracts the earth, why does the earth not move towards the moon?

Answer: The Moon exerts a gravitational force on the Earth, the reason the Earth does not move towards the Moon is because the Earth's mass is larger than the Moon's. The Earth's greater mass resists the gravitational pull from the Moon, keeping the Earth in its orbit.

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?

Answer: (i) If the mass of one object is doubled, the force between the objects will also double.

(ii) If the distance between the objects is doubled, the force between them becomes one-fourth (1/4) of its original value. If the distance is tripled, the force becomes one-ninth (1/9) of its original value.

(iii) If the masses of both objects are doubled, then the force between two object will be four times .

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

Answer: The importance of universal law of gravitation are :

(i) the force that binds us to the earth;

(ii) the motion of the moon around the earth;

(iii) the motion of planets around the Sun; and

(iv) the tides due to the moon and the Sun.
8. What is the acceleration of free fall ?

Answer: The acceleration of free fall is the rate at which an object speeds up when it falls towards the ground due to gravity .
9. What do we call the gravitational force between the earth and an object?

Answer: The gravitational force between the Earth and an object is commonly referred to as weight. Weight is the force with which the Earth pulls objects towards its center due to gravity.
10. Amit buys few grams of gold at the 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.]

Answer: No, the friend will not agree with the weight of gold bought. The weight of an object depends on the force of gravity acting on it. The value of gravity (g) is greater at the poles than at the equator. Since weight is directly proportional to gravity, the weight of the gold purchased at the poles will be greater than its weight at the equator.
11. Why will a sheet of paper fall slower than one that is crumpled into a ball?

Answer: A sheet of paper falls slower than a crumpled paper ball because the air resistance or drag force is greater on the flat surface of the sheet. The crumpled ball has a more compact shape with less surface area, allowing it to experience less air resistance and fall faster.
12. Gravitational force on the surface of the moon is only 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?

Solution: The acceleration due to gravity on Earth = 9.8 m/s²,

The acceleration due to gravity on the moon 1.63 m/s².

Weight on Earth:

Weight = mass × acceleration due to gravity

Weight = 10 kg × 9.8 m/s²

Weight = 98 N

Weight on the Moon:

Weight = mass × acceleration due to gravity

Weight = 10 kg × 1.63 m/s²

Weight = 16.3 N

Therefore, the weight of a 10 kg object would be approximately 98 Newtons on Earth and approximately 16.3 Newtons on the moon .

13. 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.

Solution: Given, m/s , m/s ,

(i) Maximum Height: We have,

Therefore, the maximum height to which the ball rises is 122.5 meters.

(ii) Total Time of Flight: We have,

Therefore, the total time it takes for the ball to return to the surface of the Earth is 5 seconds.

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.

Solution: Given, m/s , ,

We have,

m/s

Therefore, the final velocity of the stone just before touching the ground is 19.6 m/s.

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

Solution: Given, m/s , m/s and

We have,

Therefore, the maximum height reached by the stone is 80 meters.

The net displacement is the vector distance from the starting point to the ending point.

Since the stone returns to the starting point, the net displacement is zero.

The stone goes up to the maximum height and then returns back to the starting point.

Total distance covered meters.

16. Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = kg and of the Sun = kg. The average distance between the two is m.

Solution: Given, the mass of the earth kg

The mass of the Sun kg.

The average distance between the earth and Sun m.

The gravitational constant

Using Newton's law of universal gravitation,

Therefore, the force of gravitation between the Earth and the Sun is N .

17. 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.

Solution: Given,

For the stone falling from the top of the tower : Here, m/s

We have,

For the stone projected vertically upwards from the ground: Here, m/s ,,

We have,

Adding (i) and (ii) , we get

From (i) , we get

Therefore, the two stones will meet after 4 seconds, and they will meet at a height of 80 meters above the ground .

18. 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 4 s.

Solution: (a) Given, m/s ,, , seconds

m/s

Therefore, the ball was thrown up with an initial velocity of 29.4 m/s.

(b) We have, , m/s , m/s²

Therefore, the maximum height reached by the ball is 44.1 meters.

Therefore, after 4 seconds, the ball is 39.2 meters below its starting point.

(a) The velocity with which the ball was thrown up is 29.8 m/s.

(b) The maximum height reached by the ball is 44.1 meters.

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

Answer: The buoyant force on an object immersed in a liquid always acts in the upward direction, opposite to the force of gravity.

20. Why does a block of plastic released under water come up to the surface of water?

Answer: Due to the block's density being lower than that of water, the buoyant force exerted on the block is greater than its weight, causing it to float and rise to the water's surface.

21. The volume of 50 g of a substance is 20 . If the density of water is 1 , will the substance float or sink?

Solution: Given, the mass of the substance = 50 g

The volume of the substance = 20 cm³

Density

Density = 2.5 g/cm³

Since the substance's density is greater than that of water, it will sink when placed in water.

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

Solution: Given, the mass of the packet = 500 g

The volume of the packet = 350 cm³

We know that, Density

Density

Density = 1.43 g/cm³

Since the packet's density is greater than that of water, it will sink when placed in water.

Therefore, the mass of the water displaced by the packet is 500 g.