Gravitation - Physics For Class IX (Science Group) - Self Assessment Questions and Test book Exercise

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Physics For Class IX (Science Group)
UNIT 6: GRAVITATION
Self Assessment Questions and Test book Exercise

Self Assessment Questions

Q.1: What will be the effect on gravitational pull between two objects if medium between them is changed?
Ans: The gravitational force present between the two masses will always remain the same no matter whether the masses are in air, vacuum, water, or separated by some hindrance. Because, the gravitational force is not dependent on the intervening medium. Therefore, there will be no effect on the gravitational pull between two objects if the medium between them is changed.

Q.2: Which force causes the moon to move in orbit around earth?
Ans: When an object moves in a circle at a constant speed, its direction constantly changes. A change in direction causes a change in velocity. This is because velocity is a vector quantity. It has an associated direction as well as a magnitude. A change in velocity results in acceleration, so an object moving in a circle is accelerating even though its speed may be constant. An object will only accelerate if a resultant force acts on it. For an object moving in a circle, this resultant force is the centripetal force that acts towards the middle of the circle.
The gravitational attraction provides the centripetal force needed to keep planets in orbit around the Sun and all types of satellites in orbit around the Earth. The Earth's gravity keeps the Moon orbiting us. It keeps changing the direction of the Moon's velocity. This means gravity makes the Moon accelerate all the time, even though its speed remains constant.

Q.3: Why weight of an object is different at different planets?
Ans: An object's weight is dependent on its mass and the strong gravitational pull of the planet on which it is standing on. In other words, Every object in the universe with mass attracts every other object with mass. Mass of an object only depends on the constituent matter of an object and is independent of other factors. The mass of an object will always be a non-zero value.
While the acceleration due to gravity of planet (or any other object’s) is caused due to the gravitational pull of that planet and depends on its size, mass, and density. It has different values at different places.
Therefore, The weight of the same object is different on different planets because weight depends on the gravitational force of the planet and gravitational force on every planet is different so the weight also differs from planet to planet. the higher the gravity the higher our weight.

Q.4: What is the actual value of 'g' near the surface of Earth?
Ans: Near Earth's surface, gravitational acceleration is approximately 9.81 ^m/_s², which means that ignoring the effects of air resistance, the speed of an object falling freely will increase by about 9.81 metres per second second.

Q.5: The strength of gravity on the Moon is 1.6 N kg . If an astronaut’s mass is 80 kg on Earth, what would it be on the Moon?
Ans: For Solution of Numericals Click Here

Q.6: If you go on a diet and lose weight, will you also lose mass? Explain.
Ans: Let us imagine a surface that just barely surrounds our body as if we shrink-wrapped a body in plastic, by the law of conservation of mass the only way our body can lose any amount of mass is for that amount of mass to pass out through the surface. So we just have to consider what bodily functions cause that to happen:

1. Exhaling
2.  Sweating
3. Excretion (in the non-technical sense of, roughly, things we do in the bathroom)

Any dead skin cells, strands of hair. etc. that fall off we would also count. As a bonus the "shrink-wrap view" also makes it easy to identify how we gain mass, by looking for all processes that cause matter to be drawn in through the invisible surface:

1. Eating and drinking: solids and liquids through the esophagus and gastrointestinal tract.
2. Inhaling gas through the trachea and lungs.

The thing is, when most people talk about losing weight, they're referring to a long term average loss of mass, which means that the processes in the first list have to remove more mass over some extended period of time than the ones in the second list bring in. This requires some of the ore-existing mass in our body to be converted into the waste forms that we can dispose of through excretion, exhaling and sweating. This generally tends to be body fat. The other answers do a pretty good job filling in the fat gets converted to waste products.

Q.7: What will be the value of acceleration due to gravity on the surface of earth if its radius reduces to half?
Ans: For Solution of Numericals Click Here

Q.8: What will be acceleration due to gravity on the surface of earth f its mass reduces by 25%?
Ans: For Solution of Numericals Click Here

Q.9: What will be the mass of a planet whose radius is 20% of the radius of earth?
Ans: For Solution of Numericals Click Here

Q.10: Write down any four uses of artificial satellites.
Ans: USES OF ARTIFICIAL SATELLITE:
Artificial satellites carry instruments, passengers or both to perform different experiments in space. They are used for different purposes like:

• For communication.
• For making star maps.
• For making maps of planetary surfaces.
• For collecting information about weather.
• For taking pictures of planets, etc.

Q.11: What is Geostationary orbit?
Ans: GEOSTATIONARY ORBIT:
A communication satellite completes its one revolution around the Earth in 24 hours. As Earth also completes its one rotation about its axis in 24 hours, therefore the communication satellite appears to be stationary with respect to Earth. The orbit of communication satellite is therefore called “Geostationary orbit”. The height of a geostationary satellite is about 42,300 km from the surface of the Earth. Its velocity with respect to Earth is zero.

Q.12: Why the two satellites of different masses have same speed in the same orbit?
Ans: We know that the velocity that a satellite must possess when orbiting around the Earth in an orbit of radius (r = R + h) is:

This shows that the speed of the satellite is independent of its mass. Hence every satellite whether it is very massive (large) or very light (small) has the same speed in the orbit. Hence, the two satellites of different masses have the same speed in the same orbit.

Text Book Exercise

Section (B) Structured Questions
Newton’s Law of Gravitation
1.a) Why we do not feel the gravitational force of attraction from the objects around us?
Ans: We do not feel the gravitational force of attraction between objects around us due to the very small value of `G'. But it exists everywhere in the universe. Gravitational force is a weak force unless large masses are involved. The masses of humans are quite small and thus the magnitude of gravitational force is also very small and negligible as compared to that shown by the Earth. Thus, gravitational force exists between two people sitting close by but it is negligible and cannot be felt.

1.b) Define Gravitational field with an example.
Ans: GRAVITATIONAL FIELD:
Gravitational field can be described as:
“A gravitational field is a region in which a mass experiences a force due to gravitational attraction”.

EXAMPLE:
Earth's Gravitational Field:
The earth has an attractive gravitational field around it. Any object near the Earth experience this force which is due to Earth's gravity. This field is directed towards the centre of the Earth.
Field force Of Earth's Gravitational Field:
The force of this field is strongest near the surface of the Earth and gets weaker as we move farther and farther away from the Earth. This force is called the “Field Force” because it acts on all objects whether they are in contact with Earth's surface or not. So, it is a non-contact force.
For example,
It acts on an aeroplane either it is standing on Earth's surface or flying in the sky.


2.a) Write down any three characteristics of Gravitational force?
Ans: CHARACTERISTICS / KEY POINTS OF GRAVITATIONAL FORCE:
Gravitational force has following characteristics:

1. It is always present between every two objects because of their masses.
2. It exists everywhere in the universe.
3. It forms an action-reaction pair.
4. It is independent of the medium between the objects.
5. It is directly proportional to the product of the masses of objects.
6. It is inversely proportional to the square of the distance between the centres of the objects. Hence it follows the “Inverse Square Law”.

(Note: Write down any three characteristics as mentioned in question.)

2.b) Define gravitational field strength.
Ans: Gravitational Field Strength:
A body of mass one kilogram (1 kg) on Earth experiences a force of about ten newton (10 N) due to Earth's gravitational field. This force determines the gravitational field strength which is defined as:
"Gravitational field strength ‘g’ is the gravitational force acting per unit mass."
The gravitational field strength “g” is approximately 10 Newton per kilogram or 10 Nkg^-1. The gravitational field strength “g” is different at different planets.
For example,
The gravitational field strength “g” on the surface of Moon is approximately 1.6 Newton per Kilogram 1.6 Nkg^-1.

Gravitational Field Strength Of Different Planets:
Acceleration due to gravity “g” at different planets are as follows:

Planet	Value of g ms-2
Earth	10
Moon	1.62
Venus	8.87
Mars	3.77
Jupiter	25.95
Sun	274
Mercury	3.59
Saturn	11.08
Uranus	10.67
Neptune	14.07

3.a) State & explain Newton's law of gravitation?
Ans: NEWTON'S LAW OF GRAVITATION:
Sir Isaac Newton, was one of the greatest scientist of the world. He made fundamental contributions not only to several branches of Physics (like optics and mechanics) but also to Astronomy and Mathematics. He formulated the laws of motion and law of Universal gravitation.

Statement Of Newton’s Law Of Gravitation:
Newton's law of universal gravitation states that:

"Everybody in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres."

EXPLANATION:
Derivation of Newton's Law Of Gravitation:
To understand this law, let us consider two bodies of masses m₁ and m₂. The distance between their centers is r.
According to the statement force of attraction between two bodies is directly proportional to the product of their masses.

Therefore,

F ∝ m₁ m₂ ------- (i)

The gravitational force of attraction is inversely proportional to the square of the distance between the centers of the masses of the bodies. Therefore

Where 'G' is constant of proportionality known as “Universal gravitational constant” or Newtonian constant of gravitation or the Cavendish gravitational constant.

Unit Of Universal Gravitational Constant:
The value of ‘G’ in SI unit is 6.673 x10^-11 Nm²kg^-2. This is very small value. ‘G’ remains constant everywhere.

We do not feel the gravitational force of attraction between objects around us due to the very small value of 'G'. But it exists everywhere in the universe.

3.b) Define 'field force'.
Ans: FIELD FORCE:
In physics, a field force is a vector field that describes a non-contact force acting on all objects whether they are in contact with surface or not at various position in space or on Earth.

4. Determine the gravitational force of attraction between Urwa and Ayesha standing at a distance of 50m apart. The mass of Urwa is 60 kg and that of Ayesha is 70 kg.
Ans: For Solution of Numericals Click Here

Weight
5.a) Why weight of an object does not remain same every where on Earth?
Ans: The weight of a body is the gravitational force on it.

Mathematically, W = mg.

Thus, weight is dependent on gravitational acceleration, g or gravity. Hence, the weight of a body will change from one place to another place because the value of g is different in different places. Gravity is often assumed to be the same everywhere on Earth, but it varies because the planet is not perfectly spherical or uniformly dense. Earth's gravity is weaker at the equator due to centrifugal forces produced by the planet's rotation. It's also weaker at higher altitudes, further from the planet's centre. Therefore, the weight of an object does not remain the same everywhere on the Earth.

5.b) Why the unit of weight is Newton? Explain.
Ans: The weight of an object is the force of gravity on the object and may be defined as the mass times the acceleration of gravity, i.e. w = mg. Since the weight is a force, its SI unit is the newton.

6.a) Define weight and write down its equation?
Ans: WEIGHT:
All the objects which are thrown upward in the air, fall back to the ground.
The force applied by the Earth's gravitational field, pulls the objects downward. Weight is another name for the Earth's gravitational force on the objects. Because ‘gravity’ is taken from Latin word ‘gravitas’ means ‘weight’.
Therefore weight can be defined as:

"The weight of an object is the measurement of gravitational force acting on the object."

OR

"Weight of an object is the gravitational pull of Earth acting on it."

Weight 'W' of an object of mass 'm', in a gravitational field of strength 'g' is given by the relation:

W = mg .......... (i)

Unit Of Weight:
Like other forces, weight is a vector quantity and is also measured in Newton's (N).

6.b) Weight of Rani is 450N at the surface of Earth. Find her mass?
Ans: For Solution of Numericals Click Here

7. Weight of Naveera is 700N on the Earth's surface. What will be Naveera's weight at the surface of Moon?
Ans: For Solution of Numericals Click Here

8.a) Your weight decreases as you go up at high altitudes, without dieting. Explain.
Ans: A we know that weight is equal to mass times gravitational acceleration. If we move up to higher altitude the distance between us and the earth increases. Since the gravitational force is inversely proportional to distance, thus the gravitational force exerted on our body decreases as we go up at high altitudes, without dieting and so our weight also decreases.

8.b) If you step on a scale and it gives reading 55 kg, is that a measure of your weight. If not then which physical quantity it shows?
Ans: The terms "balance" and "scale" are often used interchangeably, and most of us would have a bit of trouble nailing down the characteristics of each. There are technical and practical differences between the two, including exactly the quantity is being measured and the types of applications are used for. Although the terms "balance" and "scale" are used interchangeably, technically they measure different things.

Balances Measure Mass: Balances are instruments that measure mass (basically the amount of matter in something). A true balance measures mass directly by comparing the unknown mass to a known mass, a process that is not affected by changes in gravity. A balance of this sort will give the same reading irrespective of location because gravity will act on both sides of the balance equally.

Scales Measure Weight: Scales measure weight, which is the force acting on a mass that is equal to the object's mass times its acceleration due to gravity. A scale can't measure mass directly, because the weighing mechanism and the weight of any given object are dependent on local gravity. On the Earth, gravitational acceleration can vary by as much as 0.5%, changing with distance from the Earth's core, as well as the latitudinal way. From a practical viewpoint, once a scale has been calibrated at its location, gravity is assumed or ignored. Therefore, weights are reported in mass units like kilograms, even though weight is a measurement of force using the newton. This also allows for the use of the terms "weight" to refer to both weight and mass, and "weigh" can be the process of determining either.

Mass of Earth
9. Calculate the mass of Earth by using Newton's law of gravitation.
Ans: MASS OF THE EARTH:
Mass of Earth can not be measured directly by placing it on any weighing scale. But it can be measured by an indirect method. This method utilizes the Newton's law of universal gravitation.
Let us consider a small ball is placed on the surface of Earth.

• m ⟶ Mass of the ball.
• M_E ⟶ Mass of Earth.
• G ⟶ Universal gravitational constant.
• R_g ⟶ Radius of earth; which is also the distance between the ball and centre of earth.

Then according to Newton's law of universal gravitation, the gravitational force F of the Earth acts on the ball is:

Whereas the force with which Earth attracts the ball towards its centre is equal to the weight of the ball.
Therefore,

F = W = mg ............. (ii)

Comparing equation (i) and (ii); we get:

Numerical values of the constants at right hand side of equation (iii) are:

• g = 10 Nkg^-1
• R_E = 6.38 x 10⁶m
• G = 6.673 x 10^-11Nm²kg^-2

Substituting these values in equation (iii), we get:

M_E = 6.0 x 10²⁴kg.

Thus, mass of Earth is 6.0 x 10²⁴kg.

10. If “M ” is the mass of Earth, “R ” radius of Earth, “G” is universal gravitational constant, then find acceleration due to gravity “g”;
i) On the surface of Earth.
ii) At the centre of Earth.
Ans: For Solution of Numericals Click Here


11. A planet has mass four times of Earth and radius two times that of Earth. If the value of “g” on the surface of Earth is 10 ms^–2. Calculate acceleration due to gravity on the planet.
Ans: For Solution of Numericals Click Here

12. Evaluate the acceleration due to gravity in terms of mass of Earth “M_E”, radius of Earth “R_E” and universal gravitational constant “G”:
i) At a distance, twice the Earth's radius.
ii) At a distance, one half the Earth's radius.
Ans: Solution:
Data:

• Mass of Earth = M_E
• Radius of the Earth = R_E
• and Universal gravitational constant = G

Artificial Satellite
13.a) Calculate the speed of a satellite which orbits the Earth at an altitude of 400 kilometers above Earth's surface.
Ans: For Solution of Numericals Click Here

13.b) Write the name of any one natural satellite.
Ans: Moon is a natural satellite because it revolves around the Earth naturally.

14.a) Write down the names of four different types of orbit.
Ans: Types of Orbit:

1. For communication.
2. Low- Earth orbit.
3. Medium- Earth orbit.
4. Geostationary orbit.
5. Elliptic orbit.

(Note: Write down any four as mentioned in question)

b) Define the terms
i) Critical Velocity.
ii) Communication Satellite.
Ans: (i) Critical Velocity:
It is defined as:

"The constant horizontal velocity required to put the satellite into a stable circular orbit around the Earth."

It is also known as orbital speed or proper speed.
Mathematically,

v_c = √ gR 

Where,

• v_c = Critical velocity
• g = Acceleration due to gravity on the surface of Earth.
• R = Radius of Earth

ii) Communication Satellite:
An artificial satellite which completes its one revolution around the Earth in 24 hours is used for communication purpose. As it is used for communication purpose, therefore it is known as “Communication Satellite”.

15. Derive the expression for the motion of a satellite. v = √ GM/R + h 
Ans: Expression For The Velocity That A Satellite Possess When Orbiting Around The Earth:
Let us consider the motion of a satellite which is revolving around the Earth:

• m ⟶ Mass of the satellite.
• M ⟶ Mass of Earth.
• R ⟶ Radius of Earth
• h ⟶ Height (altitude) of satellite from the surface of Earth.
• r = R + h ⟶ Radius of orbit.

Then, as we already discussed:

This gives the velocity that a satellite must possess when orbiting around Earth in an orbit of radius (r = R+h).
This shows that, the speed of the satellite is independent of its mass. Hence every satellite whether it is very massive (large) or very light (small) has the same speed in the same orbit.

16.a) Differentiate between the natural satellite and artificial satellite.
Ans: Difference Between Natural Satellite And Artificial Satellite:

S.NO.	Natural Satellite	Artificial Satellite
1.	The planet which revolves around another planet naturally is called “Natural Satellite”	The object which are sent into space by scientists to revolve around the Earth or other planets are called “Artificial Satellite”.
2.	E.g: Moon is a natural satellite because it revolves around the Earth naturally.	E.g. Sputnik-1, Explorer-1 are amongst the artificial satellites.

16.b) Name the parameters on the basis of which orbits are characterized.
Ans: PARAMETERS FOR ORBITS:
Orbits are characterized on the basis of different parameters like,

• Their distance from the Earth,
• Their time period around the Earth etc.