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Detailed notes on the topic Gravitation

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  1. 1. GravitationHello FriendsLet us first understand as to what do we mean by the word Gravitation.What is Gravitation?Gravity, also called gravitation, is a force that exists among all material objects in the universe. Forany two objects or particles having nonzero mass , the force of gravity tends to attract them towardeach other. Gravity operates on objects of all sizes, from subatomic particles to clusters of galaxies.It also operates over all distances, no matter how small or great.Newton ‘s law of gravitation states that the force of attraction between particles is directlyproportional to their mass and inversely proportional to the square of distance apart.F ∝ m 1 m2 Gm1 m 2F= − r2Where G is the universal gravitational constant,G = 6.673 × 10-11m3kg-1s-2Gravitational Field Strength A gravitational field is a region where gravitational force acts on massive bodies. Eg . gravitational field of the Earth. The gravitational field strength tells us how strong a gravitational field is. The gravitational field strength of the Earth near its surface is 9.81m / s2. The gravitational field strength , E at a point is the force of gravity per unit mass exerted on a mass placed.
  2. 2. The variation of the acceleration due to gravity g’ with distance r from the centre of the Earth is illustrated by the graph above. bove.Gravitational Potential The strength of the gravitational force at a point in a gravitational field is described by the gravitational field strength E or g is a vector quantity. Another quantity associated with the point in the gravitational field is the gravitational potential. It is a scalar quantity quantity. The gravitational potential V at a point P in a gravitational field is defined as the work done per unit mass to bring a body from infinity to P. The unit for gravitational potential is Jkg¯¹. ody . Jkg The gravitational potential energy U of a body at a point P in a gravitational field is defined as the work done to bring the body from infinity to P. The unit for gravitational potential energy . is J. Hence the gravitational potential energy U of a body of mass m at a point where the gravitational potential, V is given by U = mV On the surface on the Earth, r = R – Gravitational potential, V = - otential, – Gravitational potential energy, U = - – The graph illustrates the variation of the gravitational potential V with distance r from the centre of the Earth.
  3. 3. Relationship Between g and G- G is the Universal Gravitational Constant.- It is a scalar quantity with dimension L3M-1T-2- g is the acceleration due to gravity . vity- It is a vector quantity with dimension LT-1 GMm F= R2 GMm mg = R2 GM g= 2 R gR2 = GMWhere g = acceleration due to gravity R = constant radius of earth G = universal gravitational constant M = mass of EarthSatellite Motion in Circular OrbitsSatellite is a body that revolves round a planet. Satellites can be categorized as natural satellites or sman-made satellites. The moon, the planets and comets are examples of natural satellites. madeExamples of man-made satellites are Sputnik I , Measat I ,II and III whi are communication made whichsatellites. In order to launch satellite into orbit , rockets are used. When rocket that carries thesatellite reaches the required height , the satellite is launched into circular orbit with a certainvelocity v that is tangential to intended orbit. o
  4. 4. question, solution:Lets see this question, Try to solve on your own and then look at the solution:Que. Suppose the earth increases its speed of rotation. At what new time period will the weight of a body in the equator becomes zero ? (Take g = 10 m/s2 and RE= 6400 km)Solution: The weight will become zero when g = 0 also g = g - Rw2 => g - Rw2 =0 g => w = R 2π g = T R T = 1.4 hr you’ I hope you’ll enjoyed studying Gravitation Chapter.