§ v= j2gR 1, What keeps on earth satellite moving in its orbit? (@) Burning of fuel (0) Gravitational attraction of sun (€) Gravitational attraction between satellite and earth (@) None of the above 2. A student is asked to take the simple pendulum to the 8" floor of the building from ground floor. ‘The acceleration due to the gravity and its time period will : (@) increase, decrease }) decrease, increase ly of mass m is taken to the bottom of deep . The mass of body will : Increase (B) Decrease Remain same Increase and then decrease value of “g’ on a planet : (Knowledge and Understanding Based) ee Sanding Based) (©) Depends on mass of body on planet (d)_ Both (a) and (6) 5. Time period of earth satellite in circular orbit is independent of : (@) Mass of satelite (®) Radius of its orbit (©) Both mass and radius of orbit (@ Neither mass of satellite nor radius of its orbit 6. Ifthe mass of the sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct ? (@ Time period of a simple pendulum on the earth would decrease () Walking on the ground would become more difficult (c) Raindrops will fall faster @ _‘g’ on the earth will not change 7. A comet orbits around sun in an elliptical orbit. Which of the following quantities remain constant during the course of its motion ? (@) Linear velocity (6) Angular velocity (c) Angular momentum (@) Kinetic energy(6) increase (@) decrease (a) become zero (c) become infinite 9, The gravitational force between two bodies is : (a) Conservative (b)_ Repulsive (c) both (@)and (6) (4) Non conservative 10, The examples of central force is: (@) Nuclearforce (6) Weak nuclear force (© Gravitational fore (d) None of these ‘11. The acceleration due to gravity on earth’s surface is: (@) Maximum at pole (©) Maximum at equator (©) Minimum at pole (@_ Equal at both pole and equator 12. When you go from equator to the poles, the value of acceleration due to gravity : (a) Increases (6) Decreases (©) Remains same (@)_ Decrease up to a latitude of 45° and then increases 13, Newton’s law of gravitation is applicable to (a) Bodies in solar system only (6) Bodies on earth only (©) Planets only (d@) All the bodies in the universe 14, If the radius of the earth were to shrik by 1% (Mass remaining the same) then acceleration due to gravity on the surface of earth ? (a) Will decrease (b) Will increase (©) Remains the same (d) Cannot be predicted 15. When you move from equator fo pole, the value cof mass of body : (a) Increases (©) Remains same (a) Firstly increases than decreases 16. Out of the following, the only correct statement about satellite is : (a) A satellite can not move in a stable orbit in a plane passing through the earth’s centre (b) Decreases 17. 18. 19. 20, ali 2, ACCURATE REVISION PAPERS P (b) Geostationary s equatorial plane (6) We have just one geostationary satcing global communication around the globe (d) The speed of satelite increase wit, increase in the radius of its orbit ‘The bob of simple pendulum is always pref to be spherical because : (a) It reduces air friction (b) It is convenient to manufacture. Su launched in go (©) Because of least surface area it requires ey ‘material and so it is economical (d)_Ithas least volume so gives good speed Two astronauts are floating in gravitational ng space after having lost contact with ther spaceship, The two will : (@)_ Move towards each other (8) Move away from each other (©) Will become stationary (@ Keep floating at the same distance betwen them While noting the time period of a simp pendulum, amplitude of oscillation should & kept: @_ Without any restriction (6) As small as possible (©), Reasonably large for easy measurement (d@) Very large Kelpler’s laws are based on : (a) Copemicus experiments (b) Ptolemy’s experiments (©) Tycho Brohe’s experiments (@_ Cavendish experiments Which of the following statement is core!’ Weightlessness of an astronaut moving it? satellite is situation of : (a) No gravity (6) Zero g (c)_ Free Fuel (@ Zero mass Reason for weightlessness in a satellite is (a) Zero gravity () Centre of mass (0) Zero reaction force by satellite surface (a) None of theseTHON SS 131 ANSWERS ee POF 8 a me 88 nw n@ Pe 8 O 9% 2. © 1. Ifa particle is inside a uniform spherical shel the gravitational force on the particle is zero, 2. Each planet moves around the sun in a orbit with Sun at one of the fox ular 4, Ifthe object is under the gravitational influence of another object, the linear momentum of the object is conserved. 4. An astronaut in a space satellite experiences ‘weightlessness because satelite is in the state of free fall. 1. Te . False 3. False 4 True Q.1? State law of orbits (Kepler’s First Law) ‘ns. Each planet revolves around the sun in an elliptical orbit with sun at one of the foci as ‘shown in figure. 26+ sun a of areas (Kepler's 2". Law) joining the sun and a planet sweePs out in equal intervals of time i.e. the fty of the planet around the sun Is 5. (a) 6 (dy 1 © & (b) 3. 14. (b) 15. (c) 16. (b) 21. (c) 22. (a) TRUE/FALSE TYPE QUESTIONS 5. Newton's Jaw of gravitation obeys Newton’s third law of motion 6. The Total energy of an artificial satellite in its orbit is positive. 7. Gravitational force is an example of a Central force. 8. Acceleration due to gravity increases with increasing altitude. 9. Acceleration due to gravity is independer ‘mass of earth. ant of the ANSWERS 5. True 6. False 7. True ® False a s A. State law of periods (Kepler's 5" Law) The square of the time period for a planet to complete one revolution around the sun is directly proportional to the cube of semi-major axis of the elliptical orbit, ih = ye constant Where T = time taken by the planet to go once around the sun R= semi-major axis of the elliptical orbit. Proof :Centripetal force will be provided by tional foree between planet and Earth132 Q4. Ans. Oass. Ans. force 0) Velocity of planet (v) circumference of circular orbi timeperiod ee) is gravitational force ? ‘The force of attraction between any two bodies of the universe, is called gravitational force. It was discovered by Newton in the year 1965. ‘State Newton’s law of gravitation. According to this law, each particle attracts every other particle in this universe. The force of attraction between two particles is directly proportional to the product of their ‘masses and inversely proportional to square of the distance between them. This force is called gravitational force. m m ooo es Consider two particles of masses m, and m, separated by a distance r (as shown in the figure). The force of attraction between these two particles is given by, Fo r p= es o where, Gis the universal gravitational constant. 2.6, Ans. Q8. Ans, Q.9. Ans. al constant, W, its value and dimensional formula, “ We know, F=G r If m, = m, = 1 kg, r= 1 m, then G Thus, universal gravitational constant (G) ;, numerically equal to the force of atracin between two bodies of mass I kg each separates by a distance of 1 m. SL unit of gravit jonal constant Nm? S.L unit of G= "> = Nm’ Kj Kg’ Value of G = 6.67 x 10'' Nm? Kg? ang 6.67 x 10 *dyne om*g”. Dimensional Formula of G =—M'LET?] characteristics of important gravitational force. (Gravitational force is a central force. (ii) Gravitational force is a long range force (iti) Gravitational force between two bodies i independent of the nature of the intervening medium, i») Gravitational force is attractive in nature (©) Gravitational force is a conservative for: (Vi Itis independent of the presence or abse* of other bodies. What do you understand by acceleration dv? to gravity (g) ? ‘The acceleration experienced by a body du’ Gravitational force of the earth is known ® acceleration due to gravity. It is denoted by State the factors on which ‘g’ depends. ‘g’ depends upon : () the size (or radius) of the earth ( planet). (ii) the mass of the earth (or a planet) However, value of ‘g’ does not depend mass of the body. (or the con0. Calculate the im, @ law.of Gravitation" Ans. where, a) Also, From () and (1), we have s(t) ing, =oMm R ag jeg R M = 8 G Ai) Now, We know that, & =98ms?, R = 6400 km=6.4 x 10° m G =6.67% 10" Nm? Ke? Put these values in eqn. (if) we get, 62 OD) 6.6710"! 98 x 10% kg vend M =6x 10"kg Qi. Calculate the mean density of earth. GM ao ‘ms, Weknow, = £= 77 ‘set aie R Let p be the mean density of the earth. Since "earth is assumed to be a homogeneous sphere of radius R, therefore, mass of the earth is given by M = Volume * Density Aaa ts ataR’p 3 Put this value in eqn. (i), We get i) Now, We know that, 2=98 ms? G = 6.6710" Nm? kg? R = 6400 km= 6.4 « 10° m Put these values in (if) we get, at x28; 43.142 x 6.67 x10" 6.4 x10" P=S4784 kg m = 5.4784 x 10° kg m? = 5.5 x 10°kgm~ Q12. Show that the value of “g’ at the poles of earth is greater than that at the equator. (hs ma Since, R (equator) > R (pole) Ans, Weknow, Boole * Sequator = or row Rade Pads ‘ear ‘Thus, the value of ‘g’ at the pole is more than that at the equator. Q.13. Define gravitational field and intensity of gravitational field. Write the S.J. unit and dimensional formula of the intensity of gravitational field. ‘Ans, The space around a body within which its gravitational force of attraction is experienced by other bodies is called gravitational field. ‘The intensity of gravitational field at a point in the gravitational field is defined as the force experienced by a body of unit mass placed at that point, It is denoted by E. F ie, E=— m ‘The unit of the intensity of gravitational field is N kg” or ms Dimensional formula of intensity of gravitational ir MET" = (M°LT?] we field =. Define gravitational potential energy. Gravitational potential energy of a body at a point is defined as the amount of work done in bringing a body from infinity to that point in the gravitational field. It is denoted by U. Its ‘mathematical expression is given by, [y= -GMm Q.15. Define gravitational potential, Ans. The gravitational potential at a point in the gravitational field of a body is defined as the amount of work done in bringing a body of unit ‘mass from infinity to that point in the field. It is denoted by V. ‘The unit of gravitational potential is J kg and erg ge’ ie Dimensional formula of Gravitational are eral era) mass M Q. 16. Write relation between gravitational field tensity and gravitational potential. where “ is called gravitational potential gradient. [7. Define escape speed. ‘The minimum yelocity with which a body must be projected upwards so as to enable it to just ‘overcome the gravitational pull of the earth is known as escape velocity. zak ie. 18. What is satellite ? ‘A small body revolving around a planet in an itis called satelite, There are wo types of | Satellite (ii) Artificial Satellite Je,moon revolves around the planet ‘moon is natural satellite of the earth. Q19. Ans. Q.20. Q.21. Ans. Q.22. Q.23. Ans, Define orbital velocity of satellite, The velocity required to put a satelite int, orbit around the earth is called orbital veloc A satellite moves around the earth in its orb) velocity. ie. Find the relationship between escape velociy and orbital velocity. We know, escape velocity is given by v= Pek a The orbital velocity of a body orbiting close tp -earth is given by v9 = JR Q Dividing eqn. (1) by eqn. (2), we get or v, = 2 % .B) ‘Thus, escape velocity is /2 times the orbital velocity. What is geo-stationary satellite ? ‘The satellite in an orbit which is at rest with respect to the earth is called Geo-stationay satellite and the orbit of such a satellite is known as Geo-synchronous orbit. What. are polar satellites or remote sensing satellites ? Satellites which go around the poles of the earth in north-south direction are known as polar satellites Polar satellites are not used for communiatio? purpose. They are used for remote sensing 2% hence known as remote sensing satellites. Write the uses of polar satellites or remo sensing satellites, In India, remote sensing satellites IRS-1A. be TB and IRS-IC are being used to collect the «a for the following purposes (For detecting the areas under forest (ii) For ground water survey. (iii) For the assessment of drought. (iv) For preparing wasteland mapsI, The quantity of matter contained ina body is called mass of the body. 2. Its vector quantity. 3. It is zero at the 4. Its SI unit is centre of the earth or when body falls freely. Newton (N). Gravitational Mass T. It is the measure of gravitational interaction. 2,15 Beat be measured using ‘Newton’s universal law. Q.30, Ans. Q.31, Ans, Q.32. Ans. 0.33. Ans. Q.34, Ans. Q.38. 0.36. Ans. Q.37. Ans. State principle of — superposition of fravitational forces, Gravitational force on a point mass due to umber of other point masses around it is the vector sum of the gravitational forces acting on the point mass due to other point masses. ‘What is the weight of a body at the centre of earth? Or Why weight of a body becomes zero at the centre of earth ? We=mg=0 (-- gat the centre of earth is zero) Distinguish between gravity and gravitation. The force of attraction between any two bodies is known as gravitation. On the other hand, force of attraction between the earth and a body is called ‘gravity. ‘What is the value of ‘g' on the surface of earth ? 9.8ms? ‘Where does a body weight more, at the pole or at the equator ? ‘At the pole, because W = mg and ‘g" at pole is greater than that at equator. Where does the body weight more at the surface of the earth or in a mine ? W =mg. Since value of g in a mine is less than that at the surface of the earth, so weight of the body in a mine is less than the weight of the body on the surface of the earth. Explain why tennis ball bounces higher on hills than in plains. ‘The value of ‘g’ on hills is less than that at the plains. So the weight (mg) of the tennis ball at hills i less than that atthe plains. In other words, the force with which the earth attracts the ball on hills will be less than that at the plains. ‘What is the value of escape velocity on the surface of earth ? 11.2 kms. Give two uses of polar satellites. ‘They are used for (detecting the areas under forest. ii). ground water survey.‘Ans, It is a’situation in which the obMerved weight of the body becomes zero, Q.39. What is the difference between geo-stationary satellites and polar satellites ? Ans. W Geo-Stationary Polar Satellite Satellites t 1. A satellite in an | 1. A low or medium orbit which is at| satellite is called rest with respect to | pdlar satellite, the earth is called ‘ge0-stationary satellite, 2. Time period of [2. Time period of geo-stationary polar satellite is satellite is exactly about 100 minutes. 24 hours. 3. The height of geo-| 3. The height of stationary satellite polar satellites is from the equatorial | about 500 km to plane is about | 800 km, 36,000 km. 4. Geostationary (4. Polar satellite is satellite is used in| used for remote telecommunication | sensing, so it is s0 it is called] called remote ‘communication sensing satellite. satellite, 5. Geo-stationary | 5. Polar satellite Totates from west ‘fotates around the to east direction} poles of the earth parallel to] in north-south equatorial plane, direction. Q.40. Is gravitational force central one ? Ans. Yes. Since the gravitational force between two bodies is directed along the line joining them, the force is central. Q.41. What is the value of ‘g? at the centre of the earth? a Ans. Zero. Q.42. What is the cause of absence of atmosphere on the moon? ‘Ans, Velocity of escape at moon is much smaller than that.on the surface of earth. The molecules will ACCURATE REVISION PAPERS Pg ty Q.38, What is meant by weightlessness ? Q.43. What is the time period of a geostay Hoary Ans. Q. 44, If the radius of the earth were to shrink ‘one percent, its mass remaining the s.,, what would happen to value of ‘yg’ ? ‘ ‘Ans. Since ‘g’ varies inversely as R?, it increases ae toa decrease in R. Q.45. What will be the time period of simpy pendulum in an artificial satellite ? Ans. Infinite. This is due to the reason that effec value of ‘g" inside the satelite is zero, Q. 46. Is the motion of a satellite or accelerated ? Ans, It is accelerated motion. ‘The centrpeal acceleration acts along the radius towards the centre, its orbit, uniform Q. 47. We cannot move finger without disturbing al the stars, Comment. Ans. When we move our finger, the distances of the various objects in universe from our finge change. Due to it, the gravitational force of attraction between those objects and fing changes hence the force of attraction changes ‘This will disturb the entire universe including the stars, Q. 48. A satellite revolves close to the surface of 4 Planet. How is it orbital velocity related wit velocity of escape from that planet ? Ans. Let and R be the mass and radius of planet = 2M [GM = YAR ‘ ve = 2 v9 Q.49, How will the orbital velocity of the satelli® change if it would have to be brought closer” the surface of planet ? ‘Ans, Since ‘vo? varies inversely as the square root the radius of orbit of planet, it has to be incre if'the satellite is to revolve closer. escape and'moon cannot hold any atmosphere.