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1 PagePhysics Notes Class 11 CHAPTER 8GRAVITATIONEvery object in the universe attracts every other object with a force which is called the force ofgravitation.Gravitation is one of the four classes of interactions found in nature.These are(i) the gravitational force(ii) the electromagnetic force(iii) the strong nuclear force (also called the hadronic force).(iv) the weak nuclear forces.Although, of negligible importance in the interactions of elementary particles, gravity is ofprimary importance in the interactions of objects. It is gravity that holds the universe together.Newton’s Law of GravitationGravitational force is a attractive force between two masses m1 and m2 separated by a distancer.The gravitational force acting between two point objects is proportional to the product of theirmasses and inversely proportional to the square of the distance between them.Gravitational force.where G is universal gravitational constant.The value of G is 6.67 X 10-11 Nm2 kg-2 and is same throughout the universe.The value of G is independent of the nature and size of the bodies well as the nature of themedium between them.Dimensional formula of Gis [M-1L3T-2].Important Points about Gravitation Forcewww.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more)

2 Page(i) Gravitational force is a central as well as conservative force.(ii) It is the weakest force in nature.(iii) It is 1036 times smaller than electrostatic force and 10’l8times smaller than nuclear force.(iv) The law of gravitational is applicable for all bodies, irrespective of their size, shape andposition.(v) Gravitational force acting between sun and planet provide it centripetal force for orbitalmotion.(vi) Gravitational pull of the earth is called gravity.(vii) Newton’s third law of motion holds good for the force of gravitation. It means thegravitation forces between two bodies are action-reaction pairs.Following three points are important regarding the gravitational force(i) Unlike the electrostatic force, it is independent of the medium between the particles.(ii) It is conservative in nature.(iii) It expresses the force between two point masses (of negligible volume). However, forexternal points of spherical bodies the whole mass can be assumed to be concentrated at itscentre of mass.Note Newton’s law of gravitation holde goods for object lying at uery large distances and alsoat very short distances. It fails when the distance between the objects is less than 10-9 m i.e., ofthe order of intermolecular distances.Acceleration Due to GravityThe uniform acceleration produced in a freely falling object due to the gravitational pull of theearth is known as acceleration due to gravity.It is denoted by g and its unit is m/s2. It is a vector quantity and its direction is towards thecentre of the earth.The value of g is independent of the mass of the object which is falling freely under gravity.The value of g changes slightly from place to place. The value of g is taken to be 9.8 m/s 2 forall practical purposes.The value of acceleration due to gravity on the moon is about. one sixth of that On the earthand on the sun is about 27 times of that on the earth.www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more)

3 PageAmong the planets, the acceleration due to gravity is minimum on the mercury.Relation between g and a is given byg Gm / R2where M mass of the earth 6.0 * 1024 kg and R radius of the earth 6.38 * 106 m.Acceleration due to gravity at a height h above the surface of the earth is given bygh Gm / (R h)2 g (1 – 2h / R)Factors Affecting Acceleration Due to Gravity(i) Shape of Earth Acceleration due to gravity g &infi; 1 / R2 Earth is elliptical in shape. Itsdiameter at poles is approximately 42 km less than its diameter at equator.Therefore, g is minimum at equator and maximum at poles.(ii) Rotation of Earth about Its Own Axis If ω is the angular velocity of rotation of earthabout its own axis, then acceleration due to gravity at a place having latitude λ is given byg’ g – Rω2 cos2 λAt poles λ 90 and g’ gTherefore, there is no effect of rotation of earth about its own axis at poles.At equator λ 0 and g’ g – Rω2www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more)

4 PageThe value of g is minimum at equatorIf earth stapes its rotation about its own axis, then g will remain unchanged at poles butincreases by Rω2at equator.(iii) Effect of Altitude The value of g at height h from earth’s surfaceg’ g / (1 h / R)2Therefore g decreases with altitude.(iv) Effect of Depth The value of gat depth h A from earth’s surfaceg’ g * (1 – h / R)Therefore g decreases with depth from earth’s surface.The value of g becomes zero at earth’s centre.www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more)

5 PageGravitational FieldThe space in the surrounding of any body in which its gravitational pull can be experienced byother bodies is called gravitational field.Intensity of Gravitational FieldThe gravitational force acting per unit mass at Earth any point in gravitational field is calledintensity of gravitational field at that point.It is denoted by Eg or I.Eg or I F / mIntensity of gravitational field at a distance r from a body of mass M is given byEg or I GM / r2It is a vector quantity and its direction is towards the centre of gravity of the body.Its S1 unit is N/m and its dimensional formula is [LT-2].Gravitational mass Mg is defined by Newton’s law of gravitation.Mg Fg / g W / g Weight of body / Acceleration due to gravity (M1)g / (M2)g Fg1g2 / Fg2g1Gravitational PotentialGravitational potential at any point in gravitational field is equal the work done per unit mass inbringing a very light body from infinity to that point.It is denoted by Vg.www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more)

6 PageGravitational potential, Vg W / m – GM / rIts SI unit is J / kg and it is a scalar quantity. Its dimensional formula is [L3r-2].Since work W is obtained, that is, it is negative, the gravitational potential is always negative.Gravitational Potential EnergyGravitational potential energy of any object at any point in gravitational field is equal to thework done in bringing it from infinity to that point. It is denoted by U.Gravitational potential energy U – GMm / rThe negative sign shows that the gravitational potential energy decreases with increase indistance.Gravitational potential energy at height h from surface of earthUh – GMm / R h mgR / 1 h/RSatelliteA heavenly object which revolves around a planet is called a satellite. Natural satellites arethose heavenly objects which are not man made and revolve around the earth. Artificialsatellites are those neaven objects which are man made and launched for some purposesrevolve around the earth.Time period of satelliteT 2π r3 / GM 2π (R h)3 / g [ g GM / R2www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more)

7 PageNear the earth surface, time period of the satelliteT 2π R3 / GM 3π / GpT 2π R / g 5.08 * 103 s 84 min.where p is the average density of earth.Artificial satellites are of two types :1. Geostationary or Parking SatellitesA satellite which appears to be at a fixed position at a definite height to an observer on earth iscalled geostationary or parking satellite.Height from earth’s surface 36000 kmRadius of orbit 42400 kmTime period 24 hOrbital velocity 3.1 km/sAngular velocity 2π / 24 π / 12 rad / hThere satellites revolve around the earth in equatorial orbits.The angular velocity of the satellite is same in magnitude and direction as that of angularvelocity of the earth about its own axis.These satellites are used in communication purpose.INSAT 2B and INSAT 2C are geostationary satellites of India.2. Polar SatellitesThese are those satellites which revolve in polar orbits around earth. A polar orbit is that orbitwhose angle of inclination with equatorial plane of earth is 90 .www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more)

8 PageHeight from earth’s surface 880 kmTime period 84 minOrbital velocity 8 km / sAngular velocity 2π / 84 π / 42 rad / min.There satellites revolve around the earth in polar orbits.These satellites are used in forecasting weather, studying the upper region of the atmosphere, inmapping, etc.PSLV series satellites are polar satellites of India.Orbital VelocityOrbital velocity of a satellite is the minimum velocity required to the satellite into a given orbitaround earth.Orbital velocity of a satellite is given byvo GM / r R g / R hwhere, M mass of the planet, R radius of the planet and h height of the satellite fromplanet’s surface.If satellite is revolving near the earth’s surface, then r (R h) - RNow orbital velocity,vo gR 7.92km / hif v is the speed of a satellite in its orbit and vo is the required orbital velocity to move in theorbit, thenwww.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more)

9 Page(i) If v vo, then satellite will move on a parabolic path and satellite falls back to earth.(ii) If V vo then satellite revolves in circular path/orbit around earth.(iii) If vo V ve then satellite shall revolve around earth in elliptical orbit.Energy of a Satellite in OrbitTotal energy of a satelliteE KE PE GMm / 2r (- GMm / r) – GMm / 2rBinding EnergyThe energy required to remove a satellite from its orbit around the earth (planet) to infinity iscalled binding energy of the satellite.Binding energy of the satellite of mass m is given byBE GMm / 2rEscape VelocityEscape velocity on earth is the minimum velocity with which a body has to be projectedvertically upwards from the earth’s surface so that it just crosses the earth’s gravitational fieldand never returns.Escape velocity of any objectve 2GM / R 2gR 8πp GR2 / 3Escape velocity does not depend upon the mass or shape or size of the body as well as thedirection of projection of the body.Escape velocity at earth is 11.2 km / s.Some Important Escape VelocitiesHeavenly body Escape velocityMoon2.3 km/swww.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more)

10 P a g eMercuryEarthJupiterSunNeutron star4.28 km/s11.2 km/s60 km/s618 km/s2 x 105 km/sRelation between escape velocity and orbital velocity of the satelliteve 2 voIf velocity of projection U is equal the escape velocity (v ve), then the satellite will escapeaway following a parabolic path.If velocity of projection u of satellite is greater than the escape velocity ( v v e), then thesatellite will escape away following a hyperbolic path.WeightlessnessIt is a situation in which the effective weight of the body becomes zero,Weightlessness is achieved(i) during freely falling under gravity(ii) inside a space craft or satellite(iii) at the centre of the earth(iv) when a body is lying in a freely falling lift.Kepler’s Laws of Planetary Motion(i) Law of orbit Every planet revolve around the sun in elliptical orbit and sun is at its onefocus.(ii) Law of area The radius vector drawn from the sun to a planet sweeps out equal areas inequal intervals of time, i.e., the areal velocity of the planet around the sun is constant.www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more)

11 P a g eAreal velocity of a planetdA / dt L / 2m constantwhere L angular momentum and m mass of the planet.(iii) Law of period The square of the time period of revolution of planet around the sun isdirectly proportional to the cube semi-major axis of its elliptical orbit.T2 &infi; a3 or (T1 / T2)2 (a1 / a2)3where, a semi-major axis of the elliptical orbit.Important Points(i) A missile is launched with a velocity less than the escape velocity. The sum of its kineticenergy and potential energy is negative.(ii) The orbital speed of jupiter is less than the orbital speed of earth.(iii) A bomb explodes on the moon. You cannot hear the sound of the explosion on earth.(iv) A bottle filled with water at 30 C and fitted with a cork is taken to the moon. If the cork isopened at the surface of the moon then water will boil.(v) For a satellite orbiting near earth’s surface(a) Orbital velocity 8 km / s(b) Time period 84 min approximately(c) Angular speed ω 2π / 84 rad / min 0.00125 rad / s(vi) Inertial mass and gravitational mass(a) Inertial mass force / acceleration(b) Gravitational mass weight of body / acceleration due to gravitywww.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more)

12 P a g e(c) They are equal to each other in magnitude.(d) Gravitational mass of a body is affected by the presence of other bodies near it. Inertialmass of a body remains unaffected by the presence of other bodies near it.www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more)

Physics Notes Class 11 CHAPTER 8 GRAVITATION Every object in the universe attracts every other object with a force which is called the force of gravitation. Gravitation is one of the four classes of interactions found in nature. These are (i) the gravitational force (ii) the electromagnetic force