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Physics Standard IX
Nayana Suresh B.ED. PHYSICAL SCIENCE CHRIST NAGAR COLLEGE OF EDUCATION THIRUVALLAM
The National Anthem Jana-gana-mana adhinayaka, jaya he Bharatha-bhagya-vidhata. Punjab-Sindh-Gujarat-Maratha Dravida-Utkala-Banga Vindhya-Himachala-Yamuna-Ganga Uchchala-Jaladhi-taranga Tava subha name jage, Tava subha asisa mage, Gahe tava jaya gatha. Jana-gana-mangala-dayaka jaya he Bharatha-bhagya-vidhata. Jaya he, jaya he, jaya he, Jaya jaya jaya, jaya he! PLEDGE India is my country. All Indians are my brothers and sisters. I love my country, and I am proud of its rich and varied heritage. I shall always strive to be worthy of it. I shall give respect to my parents, teachers and all elders and treat everyone with courtesy. To my country and my people, I pledge my devotion. In their well-being and prosperity alone lies my happiness.
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CONSTITUTION OF INDIA Part IV A FUNDAMENTAL DUTIES OF CITIZENS
ARTICLE 51 A Fundamental Duties-It shall be the duty of every citizen of India: (a) to abide by the Constitution and respect its ideals and institutions, the National Flag and the National Anthem; (b) to cherish and follow the noble ideals which inspired our national struggle for freedom: (c) to uphold and protect the sovereignty, unity and integrity of India; (d) to defend the country and render national service when called upon to do so; (e) to promote harmony and the spirit of common brotherhood amongst all the people of India transcending religious, linguistic and regional or sectional diversities; to renounce practices derogatory to the dignity of women: (f) to value and preserve the rich heritage of our composite culture; (g) to protect and improve the natural environment including forests, lakes, rivers, wild life and to have compassion for living creatures; (h) to develop the scientific temper, humanism and the spirit of inquiry and reform; (i) to safeguard public property and to abjure violence; (j) to strive towards excellence in all spheres of individual and collective activity so that the nation constantly rises to higher levels of endeavour and achievements; (k) who is a parent or guardian to provide opportunities for education to his child or, as the case may be, ward between age of six and fourteen years
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1.
Isn’t the earth spherical in shape? A man on the opposite side of my hemisphere- won’t he be standing upside down then? How can he stand without falling?
Have you also felt the same doubts? Let’s try to find the answer. Now drop a small stone from a height. What did you observe? • What could be the reason for the falling of the stone? 3|Page
Let’s throw it upwards. • What happens to the speed of the stone when thrown upward? • What about its speed when falling down? • Did you apply any force on the stone to bring it down? • From where did the stone get the force required for the acceleration? Let’s try finding answers to these questions. Tie a stone to a thread and suspend it from a spring balance. • What did you observe? • Why does the spring stretch down?
The earth attracts all objects towards its centre. This force of attraction is the force of gravity.
Write down instances where the force of gravity is felt. • A coconut falling from a coconut tree. • Planets revolving around the Sun. • Take a small stone of low mass and another one of slightly higher mass. Suspend them, one by one, from a spring balance.
Mass of a body is the amount of matter contained in it.
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• In which case was the reading higher? • Which of the stones experienced greater force of attraction of the earth? • Find out the factors that influences the force of mutual attraction between earth and the body. From the activities you have done, you would have understood that gravitational force depends on the mass of a body. Another factor which influences the force of gravity is the distance between the objects. It was Sir Isaac Newton who formulated a law connecting these factors. Sir Isaac Newton arrived at the law of gravitation on the basis of the observations made by Tycho Brahe, Kepler, Galileo and others. Thereafter he put forward the universal law of gravitation which is applicable to all bodies in the universe.
If all the rain drops from the sky went upwards, would we get water? Wow! Earth’s force of gravity saved us?
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Universal law of Gravitation All bodies in the universe attract each other. The force of attraction between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
m₁
m₂
d
If two bodies of masses m₁ and m₂ are separated by a distance d, then, 𝐹 ∝ 𝑚₁𝑚₂ 𝐹 ∝
1 𝑑2
Combining the two, we get 𝐹 ∝ 𝐹 =𝐺
𝑚₁𝑚₂ 𝑑2 (𝑚₁𝑚₂) 𝑑2
G is the gravitational constant. The value of G is 6.67 × 10⁻ⁱⁱ Nm²/kg². it was Henry Cavendish, a scientist, who determined the value of G for the first time through experiments.
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Sir Isaac Newton
Sir Isaac Newton was one of the prominent scientists who hast contributed much for the progress of science as an astronomer, physicist, mathematician and philosopher. His book 'Principia Mathematica' is considered to be the basic reference book of physics. Newton observed that all celestial bodies and all objects on earth obey the same universal law of motion. He formulated a new branch of mathematics called calculus. He gave theoretical basis to the discoveries of his predecessors like Tycho Brahe, Kepler and Galileo. Newton's Universal Law of Gravitation and Laws of Motion revolutionised the study of physics In an opinion survey conducted in 2005 by the Royal Society, Sir Isaac Newton was voted as the most influential person of the century. As a mark of respect unit of force has been named after him.
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Sl no 1
Mass of m1 Kg 5
Mass of m2 Kg 10
Distance between the bodies d (m) 2
Mutual force of attraction F (N) Gx
2 3 4 5 6 7
10 10 5 5 10 5
10 20 10 10 20 10
2 2 4 1 1 ½
Gx Gx Gx Gx Gx Gx
(5×10) 22
= G x 12.5
Observe Table 1.1 and find out the answers to the following questions: • Two bodies are at a specific distance so as to attract each other. How many times will the mutual force of attraction be if the mass of one of them is doubled? • What happens when the distance between the bodies is halved? • What if the mass of both the bodies are doubled? • What if the distance between the bodies is doubled?
Force of gravity According to the Law of Gravitation, the force of attraction between two bodies is F=G
(𝑚ₗ𝑚₂) 𝑑2
Here mₗ = M and m₂ = m and d = R. Therefore, the force of attraction between a body on the earth’s surface and the earth is 𝐺𝑀𝑚 𝑅2
Figure 1.1
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• Is the earth really spherical in shape? • Is the radius same everywhere? • Where on the surface is the radius maximum? • Where is it minimum? • So, what can you infer about the force of attraction felt at these regions?
Acceleration due to gravity Does the acceleration of the body change according to mass? You know that all bodies are attracted towards the centre of the earth. If m is the mass of the body and F is the force, by Newton’s Second Law, F=ma Thus a= F/m That is, objects are accelerated towards the Earth due to the force of attraction of earth. This acceleration is known as acceleration due to gravity (g). According to Newton’s law of gravitation, F =
𝐺𝑀𝑚 𝑅2
By Newton’s second law of motion, F= ma= mg So, mg = g= g=
𝐺𝑀𝑚 𝑅2 𝐺𝑀𝑚 𝑅2
÷m
𝐺𝑀 𝑅2
From this we can find that the factors that influence the value of g are • Mass of the Earth • Radius
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Acceleration due to gravity does not depend on the mass of the body. It will be the same for all the bodies falling to the earth.
Since the earth is not a perfect sphere, its radius is not the same everywhere. • Will the value of g be the same everywhere on the earth? • Where will the value of g be the maximum on the earth’s surface? • Where will it be the minimum? • What will be the value of g at the centre of the earth? The value of g at the polar regions is 9.83 m/s². it is 9.78m/s² at the equator. The average value of ‘g’ on the surface of the earth is taken as 9.8m/s² for solving the numerical problems. ➢ A stone dropped from a height of 29.49m took 3s to reach the ground. What is the value of g here? Where on the surface of the earth would this activity have taken place? Value of g on moon s = 29.49m, u = 0, t = 3s a = g =? s = ut + ½ at²
If M is the mass of the Moon and R its radius, then value of g on the Moon. g=
𝐺𝑀 𝑅2 ″
6.67×10− ×7.36×1022
29.49 = 0 x 2 + ½ x g x 3 x 3
=
29.49 = 3g
= 1.62m/s²
g = 29.49/ 3
(1.74×1066 )2
This is approximately 1/6 of the value of g on the earth.
= 9.83m/s² Since the value of g is 9.83m/s², this activity must have taken place at the polar region. 10 | P a g e
➢ A stone and a sheet of paper are dropped from a height together. Which of the following is true regarding its motion? • Both of them reach together • The paper reaches first • The stone reaches first
Lighter objects fall slowly. Galileo was the first to argue that this is due to air resistance. But he wasn’t able to prove it since there were no facilities to create vacuum. Sir Isaac Newton could prove this later through the feather and coin experiment. As shown in the figure, Newton placed a feather and a coin in a long transparent tube with closed ends. The tube was kept vertical at first and then suddenly turned upside down. The coin reached the bottom first followed by the feather a short while later. The experiment was repeated after removing the air inside the tube and it was found that both the feather and the coin reached the bottom simultaneously. The conclusion was that the feather took more time to reach the bottom due to air resistance. Thus, Galileo’s argument was proved right. Gravitational force is a mutual attractional force. Thus, when a stone falls, it attracts the earth just as the earth attracts the stone. But it is only the stone that falls; the earth does not rise up. What might be the reason?
Figure 1.2
From the equation, F = ma, if a body of mass m is acted upon by a force F, then a = F/m. 11 | P a g e
Consider a stone of mass m falling down. What is the force of attraction between the stone and the earth? Let’s see what will be the acceleration of the stone and the earth. Let M be the mass of the earth and m the mass of the stone. As there is mutual attraction between them, don’t they experience the same force? Therefore, acceleration of the earth aₑₐₜₕ = F/M and acceleration of the stone aₛₜₒₙₑ = F/m. As the mass of the earth (M) is huge when compared to that of the stone (m), the acceleration experienced by the earth will be negligibly small and that by the stone will be much greater. How will the acceleration of the object be, if it falls down due to force of gravity alone?
Mass and Weight Observe the figure. What are these devices used for? How do they differ? You know that all objects are attracted towards the centre of the earth. How will you calculate this force of attraction? The force with which a body of mass m is attracted by the earth towards its centre is F=
𝐺𝑀𝑚 𝑅2
=mx As
𝐺𝑀 𝑅2
𝐺𝑀 𝑅2
=g
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F = mg Here mg indicates the weight of the body. In other words, the weight of a body is the force with which the earth attracts the body towards its centre. Hence its unit is Newton (N).
Figure 1.3
Spring balance Figure 1.4
Mass is measured using Common balance. Spring balance is used to measure weight.
You know how the value of g on earth changes from place to place. Based on this, find out the answers for the following questions. • Where on earth does a body experiences maximum weight? What is the reason?
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• Where on earth does a body experience minimum weight? What is the reason? You have understood that the weight of an object depends on the acceleration due to gravity at that place.
Free fall What happens to a pencil when it is let go from a height? Won’t it fall down? Drill a hole at the bottom of an open bottle and fill it with water. Water goes out through the hole. Then allow the bottle to fall freely. What do you observe? Why?
Let us assess 1. A body, the mass and the weight of which were already determined at the Equator, is now placed at the Pole. In this context, choose the correct statement from the following: a. Mass does not change, weight is maximum b. Mass does not change, weight is minimum c. Both mass and weight are maximum d. Both mass and weight are minimum 2. What is meant by the terms mass and weight? 3. For a body of mass 60kg a. What is the weight on the earth? b. What is the weight on the moon? 4. Write down instances where free fall is experienced.
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Notes
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