# Gravitation

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Presented By Anhadh Singh Class: 9 th ‘A’ Roll No: 24

GRAVITATION

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1) Gravitation The force with which the earth pull objects towards itself is called Gravitational forces. i ) Gravitation may be the attraction of objects by the earth. Eg :- If a body is dropped from a certain height, it falls downwards due to earth’s gravity . ii) Gravitation may be the attraction between objects in outer space. Eg :- Attraction between the earth and moon. Attraction between the sun and planets. Gravitational Force is responsible for many phenomenon like- Holding the atmosphere about the Earth. Rain falling on the Earth. Keeping us firmly on the ground. NOTE: Force of gravitation is always the force of attraction. It is never Repulsive

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Isaac Newton Isaac Newton was born in Woolsthorpe near Grantham , England. He is generally regarded as the most original and influential theorist in the history of science. He was born in a poor farming family. But he was not good at farming . He was sent to study at Cambridge University in 1661. In 1665 a plague broke out in Cambridge and so Newton took a year off . It was during this year that the incident of the apple falling on him is said to have occurred . This incident prompted Newton to explore the possibility of connecting gravity with the force that kept the moon in its orbit. This led him to the universal law of gravitation.

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2 ) Universal law of gravitation The universal law of gravitation states that, ‘Every object in the universe attracts every other object with a force which is directly proportional to product of the masses and inversely proportional to the square of the distance between them.’ Let two objects A and B of masses M and m lie at a distance d from each other. Let F be the force of attraction between them. According to the universal law of gravitation the force between the objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. F M m (1 Eq ) F (2 Eq ) Combining Eqs . (1 ) and (2 ), we get F   M m A B d F

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Or, F = G (Eq.3) where G is the constant of proportionality and is called the universal gravitation constant. By multiplying crosswise, Eq. 3 gives F × = G M × m Or, G = ( Eq.4) The SI unit of G can be obtained by substituting the units of force, distance and mass in Eq . (4) as N . The value of G was found out by Henry Cavendish (1731 – 1810) by using a sensitive balance. The SI unit of G is N m 2 kg -2 and its value is 6.673 x 10 -11 N m 2 kg -2

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Importance of The Universal Law O f Gravitation The universal law of gravitation successfully explained several phenomena which were believed to be unconnected: the force that binds us to the earth; the motion of the moon around the earth; the motion of planets around the Sun; (iv) the tides due to the moon and the Sun.

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4) Free fall The falling of a body from a height towards the Earth under the influence of gravitational pull of the Earth is called Free fall . Galileo observed that the acceleration produced in a freely falling body is the same for all bodies and does not depend upon the mass of falling body. The uniform acceleration produced in a freely falling body due to gravitational pull of the Earth is called acceleration due to gravity and it is denoted by ‘g’.

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Acceleration due to gravity The acceleration due to gravity is denoted by g. The unit of g is same as the unit of acceleration i.e. ms -2 . It’s value changes lightly from place to place but for practical purposes it is 9.8 m/ . Calculation of Value of ‘g’ Suppose a stone of mass ‘m’ is dropped from a distance ‘R’, from the center of the Earth ‘M’. Then according to Newton’s Law of Gravitational: F = G -------- ( I ) Also, F = m ( from Newton’s second law of motion) Or, ---------- (2)

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Substituting the value of Eq.1 in Eq.2 ( cancelling out ‘m’) Since this acceleration is due to gravity

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To calculate the value of ‘g’, put values of G, M & R. g = 9.8 (approx.) Value of ‘g’ (maximum & minimum) Value of ‘g’ is actually not a constant because the earth is not a perfect sphere. Therefore the value of its radius is not the same at all the places. Since the radius of the earth at the poles is minimum, the value of ‘g’ is maximum at the poles. T he radius of the earth is maximum at the equator, therefore the value of ‘g’ in minimum at the equator. Value of ‘g’ decreases as we go inside the earth and becomes zero. It also decreases on going about surface of earth.

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5) Mass and Weight a) Mass Mass of a body is a quantity of the matter contain in it. It is the measure of inertia and hence mass is also called inertial mass . The mass of the body can never be ZERO . The SI unit of mass is ‘kg’. b) Weigh t :- The weight of a body is the force with which the earth attracts the body. The weight of a body can be ZERO. I ts SI unit is ‘N’. The force with which a body is attracted by the earth depends on its mass m and acceleration due to gravity g, F = m x g Since weight of a body is the force with which the earth attracts the body, W = F or, W = m x g NOTE: 1 kg of weight = 9.8N

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c) Difference between Mass & Weight Mass Weight 1. It is the quantity of matter contained in a body. 1. It is the force with which a body is attracted towards the earth. 2. It is a constant quantity and does not changes from place to place. 2. It varies from place to place. 3. The SI unit is ‘Kg’. 3. The SI unit is ‘N’. 4. It is a scalar quantity. 4. It is a vector quantity. 5. It is measured by a pan balance. 5. It is measured by a spring balance. 6. It cannot be zero. 6. Weight is zero at the center of earth and somewhere in the inter planetary space.

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d) Weight of an object on the moon The weight of an object on the earth is the force with which the earth attracts the object and the weight of an object on the moon is the force with which the moon attracts the object. The mass of the moon is less than the mass of the earth. So the moon exerts lesser force on the objects than the earth. The weight of an object on the moon is one sixth (1/6 th ) of its weight on the earth. Celestial body Mass (kg) Radius (m) Earth 5.98 x 10 24 6.37 x 10 6 Moon 7.36 x 10 22 1.74 x 10 6

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6) Thrust and pressure a) Thrust Thrust is the force acting on an object perpendicular to the surface. Eg :- When you stand on loose sand the force (weight) of your body is acting on an area equal to the area of your feet. When you lie down, the same force acts on an area equal to the contact area of the whole body. In both cases the force acting on the sand (thrust) is the same. b) Pressure Pressure is the force acting on unit area of a surface. Eg :- The effect of thrust on loose sand is larger while standing than while lying down. The SI unit of thrust is N/m 2 or N m -2 . It is called Pascal (Pa).

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7,a ) Pressure in fluids (Liquids and gases) Fluids exert pressure on the base and walls of the container. Fluids exert pressure in all directions. Pressure exerted on fluids is transmitted equally in all directions. b) Buoyancy ( Upthrust ) When an object is immersed in a fluid it experiences an upward force called buoyant force. This property is called buoyancy or upthrust . The force of gravity pulls the object downward and the buoyant force pushes it upwards. The magnitude of the buoyant force depends upon the density of the fluid.

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c) Why objects float or sink in water ? If the density of an object is less than the density of a liquid, it will float on the liquid and if the density of an object is more than the density of a liquid, it will sink in the liquid. Activity Take some water in a beaker. Take a piece of cork and an iron nail of the same mass. Place them on the water. The cork floats and the nail sinks. The cork floats because the density of cork is less than the density of water and the upthrust of water is more than the weight of the cork. The nail sinks because the density of the iron nail is more than the density of water and the upthrust of water is less than the weight of the nail. Cork Iron nail

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8) Archimedes’ principle Archimedes’ principle states that, ‘ When a body is partially or fully immersed in a fluid it experiences an upward force that is equal to the weight of the fluid displaced by it.’ Archimedes principle has many uses. It is used in designing ships and submarines, Hydrometers used to determine the density of liquids, lactometers used to determine purity of milk etc.

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9) Density and relative density i ) Density :- The density of a substance is the mass of a unit volume of the substance. The unit of density is kilogram per meter cube (kg m -3 ). ii) Relative density :- The relative density of a substance is the ratio of the density of a substance to the density of water. Since relative density is a ratio of similar quantities, it has no unit.

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