Kepler's Laws - 8-gravitation.docx PDF

**Kepler's laws** **1 MARKS QUESTIONS** 1. A planet moves around the sun in an elliptical orbit with the sun at one of its foci. Which physical quantity is associated with the motion of the planet remains constant with time? 2. In planetary motion, which law is consequence of the angula...

**Kepler's laws** **1 MARKS QUESTIONS** 1. A planet moves around the sun in an elliptical orbit with the sun at one of its foci. Which physical quantity is associated with the motion of the planet remains constant with time? 2. In planetary motion, which law is consequence of the angular momentum conservation? 3. When will the Kepler's law be applicable on the planets? 4. Define the Kepler's third law. **2 MARKS QUESTIONS** 5. State and explain Kepler's second law of planetary motion. 6. What is the direction of areal velocity of the earth around the sun? 7. The distance of the planet Jupiter from the sun is 5.2 times that of the earth. Find the period of the Jupiter's revolution around the sun. 8. In an imaginary planetary system, the central star has the same mass as our sun,but is brighter so that only a planet twice the distance between the earth and the sun can support life. Assuming biological evolution (including aging process etc.) on that planet similar to ours, what would be the average life span of a 'human' on that planet in terms of its natural year? The average life span of a human on the earth may be taken to be 70 years. 9. The time period of the planet of the sun is 5 hours. If the separation between the sun and planet is increased to 4 times the previous value, then what will be the new time period of the planet? 10. Out of aphelion and perihelion, where is the speed of the earth more and why? 11. Draw areal velocity versus time graph for mars. 12. A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.5×10^8^ km away from the sun? **3 MARKS QUESTIONS** 13. Prove that the angular momentum of a particle is equal to twice the product of its mass and areal velocity. Also prove the kepler's second law. 14. State and explain the kepler's laws of planetary motion. 15. \(a) The line that joins the Saturn to the sun sweeps areas A~1~, A~2~ and A~3~ in time intervals of 6 weeks, 3 weeks and 2 weeks respectively as shown in the figure. What is the correct relation between A~1~, A~2~ and A~3~ ? \(b) The time period of a planet of a star is 8 hours. What will be time period if the separation between the planet and the star is increased to 9 times the previous value? **4 MARKS QUESTIONS** 16. Sunita, a science student, was coming from school to her home. On the way she saw prayers were being done at various place. From Yamuna Bridge, she saw many people were taking dip in the Yamuna River. When she reached home, she was hungry. She asked her mother to give food, but her mother refused her saying solar eclipse is occurring and would not cook food till eclipse get over. When she tried to talk milk, she found Tulsi leaves in it. Mother again disallowed her to eat or drink anything till the eclipse is completed. She tried to perceive her mother that solar and lunar eclipse are the natural phenomenon and has no ill effect on anyone. But she was not ready to listen anything and advised her not to be unorthodox. She became frustrated and felt embarrassed at the superstitions of people and went to study. \(a) What are the values shown by Sunita? \(b) Time period of a planet around the sun is 11.6 years. How far is the planet from Sun? (the distance between sun and earth is 1.5 × 10^8^ km) \(c) Explain kepler's first law of planetary motion? **5 MARKS QUESTIONS** 17. Earth's orbit is an ellipse with eccentricity 0.0167. Thus, earth's distance from the sun and speed as it moves around the sun varies from day to day. This means that the length of the solar day is not constant throughout the year. Assume that earth's spin axis is normal to its orbital plane and find out the length of the shortest and the longest day. A day should be taken from noon to noon. Does this explain variation of length of the day during the year? **Universal law of gravitation** **1 MARKS QUESTIONS** 18. What would be the weight of the body inside the earth if it were a hollow sphere? 19. Is it possible to shield a body from gravitational effects? 20. What is the difference between inertial mass and gravitational mass of a body? 21. Work done in moving a particle round a closed path under the action of gravitation force is zero. Why? **2 MARKS QUESTIONS** 22. Two bodies of masses 4kg and 9kg are separated by a distance of 60cm. A 1kg mass is placed in between these two masses. What is its distance from 4kg mass, if the net force on 1kg is zero? 23. The earth is acted upon by the gravitational attraction of the sun. why don't the earth fall into the sun? 24. Gravitational force between two bodies is 1 N. if the distance between them is made twice, what will be the force? 25. A mass M is broken into two parts of masses m~1~ and m~2~. How are m~1~ and m~2~ related so that the force of gravitational attraction between the two parts is maximum? 26. Two uniform solid spheres of radii R and 2R are at rest with their surfaces just touching. Find the force of gravitational attraction between them if density of spheres be ρ? **3 MARKS QUESTIONS** 27. A solid sphere of uniform density and radius R exerts a gravitational force of attraction F~1~ on a particle placed at P. the distance of P from the centre of the sphere is 2R. a spherical cavity of radius R/2 is now made in the sphere. The sphere (with cavity) exerts a gravitational force F~2~ on the same particle at P. calculate the ratio F~1~/F~2~. 28. A rocket is fired from the earth towards the sun. At what distance from the earth's centre is the gravitational force on the rocket zero? Mass of the sun = 2 × 10^30^ kg, mass of the earth = 6 × 10^24^ kg. neglect the effect of other planets etc. (orbital radius = 1.5 × 10^11^ m) 29. A mass m is placed at P at a distance h along the normal through the centre O of a thin circular ring of mass M and radius r as shown in the figure. If the mass is moved further away such that OP becomes 2h, by what factor of gravitation will decrease, if h = r? 30. A body of mass M is divided into two parts m and M -- m. the gravitational force between them is maximum. Find. 31. A uniform solid sphere of mass M and radius *a* is surrounded symmetrically by a uniform thin spherical shell of equal mass and radius 2a. find the gravitational field at a distance \(a) a from the centre (b) a from the centre. 32. Determine the gravitational force of attraction between a uniform sphere of mass M and a uniform rod of length L and mass m, placed such that, r is the distance between the centre of the sphere and near end of rod. 33. A star 2.5 times the mass of the sun, collapsed to a size of 12km rotates with a speed of 1.5rps.(extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category).will an object placed on its equator remain stuck to its surface due to gravity? (mass of the sun = 2 × 10^30^ kg) 34. Suppose the gravitational force varies inversely as the n^th^ power of distance. Find the time period of a planet in circular orbit of radius R around the sun. 35. (a)During the time of Newton, many believed that nature followed different rules in other parts of the universe than here on Earth. Do you agree with this idea? (b)What role does Newton's law of gravitation play in physics? (c)Keen observation opens the gates of big discoveries. 36. Mythili was a student of class XI. She was sitting in a garden along with her grandmother, who was retired physics teacher. Suddenly she saw an orange falling from the tree. Immediately she asked her grandmother that both orange and earth experience equal and opposite forces of gravitation, then why it is: the orange that falls towards the earth and not the earth towards the orange. Her grandmother explained her the reason in a simple way. \(a) What are the values being displayed by Mythili ? \(b) What in your opinion may be the reason for this observation? **5 MARKS QUESTIONS** 37. State kepler's laws of planetary motion. Deduce Newton's law of gravitation from kepler's law. 38. Three point masses, each of mass m, rotate in a circle of radius r with constant angular velocity ω due to their mutual gravitational attraction. If any instant, the masses are on the vertex of an equilateral triangle of side a, then find the angular speed ω. 39. Three equal masses of m kg each are fixed at the vertices of an equilateral triangle ABC, as shown in figure. \(a) What is the force acting on a mass 2m placed at the centroid G of the triangle? \(b) What is the force if the mass at the vertex A is double? Take AG = BG = CG = 1m. **Acceleration due to gravity of the earth** **1 MARKS QUESTIONS** 40. If the earth were hallow, but still had the same mass and radius, would your weight be different? 41. Would we have more sugar to the kilogram at the pole or at the equator? 42. Why a body weight more at poles and less at equator? 43. Define the effect of shape of the earth on the value of g. **2 MARKS QUESTIONS** 44. State the relation between 'g' (on the surface of earth) and 'G'; in terms of the mass (M) and radius (R) of earth. 45. Write the unit of acceleration due to gravity. The radii of two planets are R and 2R and their densities are ρ and ρ/2 respectively. Find the ratio of the acceleration due to gravity at their surfaces. 46. An astronaut on the moon measures the acceleration due to gravity to be 1.7 ms^-2^. He knows that the radius of the moon is about 0.27 times that of the earth. What is his estimate of the ratio of the mass of the earth to that of the moon? (take, acceleration due to gravity on the earth's surface as 9.8 ms^-2^) 47. Explain why one can jump higher on the surface of the moon than on the earth. 48. Determine the speed with which the earth will have to rotate on its axis so that a person on its equator weight (3/5)^th^ its present weight. Take the equatorial radius = 6400 km. **4 MARKS QUESTIONS** 49. The rocks found at or near the surface of the earth have an average density (ρ) of 3×10^3^ kg/m^3^ and radius (R) is 6.4 × 10^6^m. \(a) Make the crude assumption that the density of the earth is uniform and obtain a first approximation to the value of Universal Constant of gravitation. \(b) Is this approximation likely to yield a value that is too large or too small? \(c) (i) common upon this approximation. \(ii) Which human trait does play its role in arriving at this approximation? 50. Shweta and Richa are good friends are living in a city near the equator. Shweta went to a country located near North Pole of the earth with her parents. Her friend Richa, requested bring a gold necklace as gold was cheaper in that country. Shweta purchased the necklace. Specification about rate, size, weight, year of manufacturing was mentioned on the necklace box. Richa gave the necklace to lab where all specification were checked. Richa told Shweta that she was cheated. However Shweta explained that weight of the body at equator is less than at poles. Shweta asked Richa to return the necklace to her because she was not interested to spoil her friendship with Richa. \(a) Why is weight of the necklace less at equator than at poles? \(b) What values are displayed by Shweta? **Acceleration due to gravity below and above the surface of earth** **1 MARKS QUESTIONS** 51. Plot a graph showing the variation of g with height and depth from the surface of earth. 52. Where does body weight more: at the sea level or on the mountains? 53. Why does a tennis ball bounce higher on a hill than on plains? 54. Why does the weight of a body become zero at centre of the earth? **2 MARKS QUESTIONS** 55. Where on the earth's surface is the centrifugal acceleration due to its rotation the greatest? Where is it the least? Why? 56. The height at which the acceleration due to gravity becomes g/9 (where g = the acceleration due to gravity on the surface of the earth) find the radius of earth in terms of R. 57. A stone weight 100N on the surface of the earth. The ratio of its weight at a height of half the radius of the earth to a depth of half the radius of the earth will be approximately. 58. How much below the surface of the earth does acceleration due to gravity become 1% of its value at the earth's surface? Radius of the earth = 6400 km. 59. How far below the earth's surface does the value of g becomes 20% of its value on the surface? 60. Show d = 2h where value of acceleration due to gravity at a height h is same as the value at a depth d. 61. At what height above the surface of earth will the value of 'g' be reduced to 81% of its value at the surface? (take the radius of the earth as 6300 km) 62. At what height above the earth's surface, the value of g would be 'nearly' the same as in a mine at a depth of r km? 63. Assuming the earth to be a sphere of radius R, find the altitude at which the value of acceleration due to gravity becomes of its value at the surface of the earth. 64. At what depth is the value of g same as at a height of 40 km from the surface of earth. 65. Find the value of g at a height of 400 km above the surface of the earth. Given radius of the earth, R = 6400 km and value of g at the surface of the earth = 9.8 ms^-2^. 66. How far away from the surface of earth does the acceleration due to gravity become 4% of its value on the surface of earth? Radius of earth = 6400 km. 67. Discuss the variation of 'g' with depth. What happens to 'g' at the centre of earth? 68. If a person goes to height equal to radius of earth from its surface, what would be his weight relative to that on the earth? **3 MARKS QUESTIONS** 69. Discuss the variation of acceleration due to gravity with depth from the surface of earth by deriving correct mathematical expression. 70. Obtain an expression, relating the value of 'g' at a point situated at a height 'h' above the surface of the earth, to its value, on the surface of the earth. 71. How far away from earth does the acceleration due to gravity become 5% of its value at the earth's surface? Assume that the earth is a sphere of radius 6.4 × 10^8^ cm. how does the weight of body vary when moved from equator to pole? 72. A particle hanging from a spring stretches by 1 cm at earth's surface. How much will the same particle stretch the spring at a place 800 km above the earth's surface? Radius of the earth is 6400km. 73. At what height above the surface of the Earth, acceleration due to gravity will be 50% of its value on the surface of the Earth? (Radius of earth is 6400 km and acceleration due to gravity on the surface of the Earth is 9.8 m/s^2^).how does the value of acceleration due to gravity depend on the depth below the surface of the earth? 74. How much above the earth surface does the acceleration due to gravity reduce by 36% of its value on the earth surface? Take the value of radius of earth 6400 km? **5 MARKS QUESTIONS** 75. \(a) Derive an expression showing variation of acceleration due to gravity with height. \(b) (i) a body weight 63N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth? \(ii) Assuming the earth to be a sphere of uniform mass density, how much would a body weight half way down to the centre of the earth if it weighed 250N on the surface? 76. How will the value of g be affected if \(i) The rotation of the earth stops \(ii) The rotational speed of the earth is doubled \(iii) The rotational speed of the earth is increased to seventeen times its present value? **Gravitational potential energy** **1 MARKS QUESTIONS** 77. In case of Earth, at what points is its gravitational field zero and at what points is gravitational potential zero? 78. What is the value of gravitational potential at infinity? **2 MARKS QUESTIONS** 79. A body of mass m is taken from the earth's surface to the height equal to twice the radius (R) of the earth. What will be the change in potential energy of body? 80. Find the work done in shifting a particle of mass m from the centre of the earth to the surface of the earth (where M is the mass of the earth and R is the radius of the earth). 81. If a body of mass m has to be taken from the surface of earth to a height h = R, then find the amount of energy required (R is the radius of earth). 82. Differentiate between gravitational potential and gravitational potential energy. 83. Two bodies of masses 10 kg and 1000 kg are at a distance 1 m apart. At which point on the line joining them will the gravitational field intensity be zero? **3 MARKS QUESTIONS** 84. \(a) what is meant by \(i) Gravitational field strength (ii) gravitational potential? \(b) What is the is the gravitational field strength of a planet where the weight of a 60 kg astronaut is 300 N ? 85. Two bodies of masses m~1~ and m~2~ are placed at a distance r apart. Show that at the position where the gravitational field due to them is zero, the potential is given by 86. At a point above the surface of the earth, the gravitational potential is -5.12×10^7^ J/kg and acceleration due to gravity is 6.4 m/s^2^.Assuming the mean radius of the Earth to be 6400 km, calculate the height of the point above the Earth's surface. 87. Mass M of a planet is uniformly distributed over a spherical volume of radius R. calculate the energy needed to deassemble the planet against the gravitational pull amongst its constituent particles. Given MR = 2.5×10^31^ kg m and g = 10 m/s^2^. 88. What is the potential energy of a body of mass m relative to the surface of Earth of radius R at : (a) a height h = R, above its surface (b) depth d = R, below its surface? 89. Two identical heavy spheres are separated by a distance 10 times their radii. Determine the potential at the midpoint. Is an object placed at that point in stable or unstable equilibrium? 90. Two stars each of one solar mass (=2×10^30^kg) are approaching each other for a head on collision. When they are at a distance of 10^9^ km, their speeds are negligible. What is the speed with which they collide? The radius of each star is 10^4^ km. assume the star to remain undistorted until they collide.(use the known value of G). 91. Find the potential energy of a system of four particles each of mass m, placed at vertices of the square of side l. also obtain the potential at the centre of the square due to four masses. 92. What will be the potential energy of a body of mass 50kg at a distance 2×10^10^m from the centre of the earth? Find the gravitational potential at this distance? **5 MARKS QUESTIONS** 93. There are three identical point mass bodies each of mass m located at the vertices of an equilateral triangle with side r. they are exerting gravitational force of attraction on each other, which can be given by Newton's law of gravitation. Potential at a point in a gravitational field is the amount of work done in bringing a unit mass body from infinity to the given point without acceleration as shown in figure. \(i) At what speed must they more if they all revolve under the influence of one another's gravitation in a circular orbit circumscribing the triangle still preserving the equilateral triangle? \(ii) How much work is done in taking one body far away from the other two bodies? 94. What is meant by gravitational potential energy of a body? What is the zero level of potential energy? Derive an expression for the gravitational potential energy of a body of mass m located at distance r from the centre of the earth. **Escape Speed** **1 MARKS QUESTIONS** 95. A rocket is fired from a deep mine inside earth so as to escape the earth's gravitational field. What is the minimum velocity to be imparted to the rocket? 96. Why do different planets have different escape velocity? 97. The escape velocity for a satellite is 11.2 km s^-1^. If the satellite is launched at an angle of 60^0^ with the vertical, what will be the escape velocity? **2 MARKS QUESTIONS** 98. The escape speed on Earth is 11.2 km/s. what is its value for a planet having double the radius and eight times the mass of the Earth? 99. A particle is projected upward from the surface of the earth (radius R) with kinetic energy equal to half the minimum value of energy needed for it to escape. To which height does it rise above the surface of the earth? 100. The escape speed of a projectile on the earth's surface of 11.2 km s^-1^. A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun and other planets. 101. The escape velocity of a projectile on the Earth's surface is 11.2 km s^-1^. A body is projected out with thrice this speed. What is the speed of the body far away from the Earth, i.e., at infinity? Ignor the presence of the Sun and other planets etc. 102. A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. the mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. What is the minimum value of u so that the particle does not return back to earth? 103. The escape velocity of a body on the surface of earth is 11.2 km s^-1^.if the earth mass increases to twice its present value and the radius of the earth becomes half, what would be its escape velocity? **3 MARKS QUESTIONS** 104. The escape velocity form the surface of earth is 11.2 km s^-1^. What is escape velocity in a planet whose radius is three times that of earth and on which the acceleration due to gravity is three times that of on earth? Does escape velocity depend on the mass of the body? 105. An object is thrown vertically upwards from the surface of the earth, with a speed of v~0~. Its speed at a height h ( where h \ i. What qualities of Ajay do you like? ii. Calculate the escape speed on the surface of planet of mass 7.5×10^25^ g; its radius is 1.6×10^6^ m. (G = 6.6×10^-8^ dyne cm^2^ g^-2^) iii. What are the conditions under which a rocket fired from the earth launches an artificial satellites **Earth Satellite** **1 MARKS QUESTIONS** 111. A satellite of small mass burns during its descent and not during ascent. Why? 112. Is it possible to place an artificial satellite in an orbit such that it is always visible over New Delhi? 113. Why are space rocket usually launched from west to east in the equatorial plane? 114. Two satellites are at different heights. Which would have greater velocity? 115. What is a parking orbit? **2 MARKS QUESTIONS** 116. What are conditions under which a rocket fired from earth becomes a satellite of the earth and orbits in a circle? 117. What is the relation between orbital and escape velocities? 118. Assuming density d of planet to be uniform, find the time period of its artificial satellite. (Assume that satellite is orbiting close to the planet's surface) 119. What is a period of revolution of earth satellite? Ignore the height of satellite above the surface of earth. (Given: the value of gravitational acceleration g = 10 ms^-2^.Radius of earth R~E~ = 6400 km. take π = 3.14) 120. By what factor does this escape velocity differ from the orbital velocity of a (near by) satellite? 121. You are given the following data: g = 9.81 ms^-2^. R~E~ = 6.37×10^6^ m, the distance to the moon R = 3.84×10^8^ m and the time period of the moon's revolution is 27.3 days. Obtain the mass of the earth M~E~ in two different ways. **3 MARKS QUESTIONS** 122. Show that the orbital time period of a planet is proportional to the 3/2 power of the radius of its orbit. 123. Define orbital velocity of a satellite. Derive expressions for the orbital velocity of a satellite. Show that the escape velocity of a body from the earth's surface is √2 times its velocity in a circular orbit just above the earth's surface. 124. The planet mars has two moons, phobos and deimos. (i) phobos has a period of 7 h 39 min and an orbital radius of 9.4×10^3^ km. calculate the mass mars.(ii) assume that earth and mars move in circular orbits around the sun, with the Martian orbit being 1.52 times the orbital radius of the earth, what is the length of the Martian year in days? **4 MARKS QUESTIONS** 125. Shobhit went to a hill station with his family. On this way, he was fascinated by the beauty of mountains all around him. But a question started creeping in his mind that how such roads creeping in his mind that how such roads have been made in the mountains which seem so unapproachable. He asked his father the same question who told his about remote sensing satellites which are used to get information of places which can't be reached directly. i. What values do you associate with Shobhit? ii. A remote sensing satellite of the earth in a circular orbit at a height of 400 km above the surface of the earth. What is the (a) orbital speed and (b) period of revolution of satellite? (Radius of the earth = 6 × 10^6^ m and g =10 m/s^2^). \(iii) What kind of the orbit does remote sensing satellite follows? **5 MARKS QUESTIONS** 126. Derive expressions for time period, altitude and angular momentum of a satellite revolving around the Earth. Briefly describe the launching of a satellite. 127. Calculate the height of a satellite from the surface of the earth so that its radial acceleration will be half the value of g at the surface of the Earth. Also calculate the velocity and the time period of the satellite. 128. A rocket is fired 'vertically' from the surface of Mars with speed of 2 km s^-1^. If 20% of its initial energy is lost due to Martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it? Mass of mars = 6.4 × 10^23^ kg. radius of mars = 3395 km; G = 6.67×10^-11^ N m^2^ kg^-2^. **Energy o an Orbiting satellite** **1 MARKS QUESTIONS** 129. Define binding energy of a satellite. 130. How much energy is required by a satellite to keep it orbiting? Neglect air resistance. 131. Can energy of the satellite be positive or zero? **3 MARKS QUESTIONS** 132. Find the expression of a total energy of a satellite revolving around the surface of the earth. What is the significance of negative sign in the expression. 133. A star like the sun has several bodies moving around it at different distances. Consider that all of them are moving in circular orbits. Let r be the distance of the body from the centre of the star and let its linear velocity be v, angular velocity ω, kinetic energy K, gravitational potential energy U, total energy E and angular momentum L. as the radius r of the orbit increases, determine which of the avove quantities increases and which ones decrease. 134. Show that the velocity of a body released at a distance r from the centre of the Earth when it strikes the surface of the earth is given by where R and M are radius and mass of the earth, respectively. Also show that the velocity with which the meteorites strike the surface of the earth is equal to the escape velocity. 135. Frictional force increases the velocity of a satellite. Discuss. 136. A 400 kg satellite is in a circular orbit of radius 2R about the earth. Calculate the energy needed to transfer it to a circular orbit of radius 4R. Find the changes in its kinetic energy and its kinetic energy and its potential energy. Give radius of earth = 6.37×10^6^ m and g=9.81 ms^-2^. **5 MARKS QUESTIONS** 137. An artificial satellite is moving in a circular orbit with speed equal to half the magnitude of escape velocity from Earth. (i) Determine the height of the satellite above the earth's surface.(ii) if the satellite is stopped suddenly in its orbit and allowed to fall freely towards Earth, find the speed with which it hits the surface of the earth. (Given radius of the earth R = 6.4×10^6^m) 138. A projectile is fired vertically from the surface of the earth with a velocity kv~e~, where v~e~ is the escape velocity and k \< 1. Neglecting air resistance, show that the maximum height to which it will rise, measured from the centre of the earth is R/(1 -- k^2^), where R is the radius of the earth. 139. Calculate the speed v with which a projectile should be launched from the surface of earth so as to reach a height equal to one fourth of Earth's radius, R. 140. A satellite is in an elliptical orbit around the earth with aphelion of 6R and perihelion of 2R where R = 6400 km is the radius of the earth. Find eccentricity of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius 6R? 141. A spaceship is stationary on mars. How much energy must be expended on the spaceship to launch it out of the solar system? Mass of the spaceship =100 kg; mass of the Sun = 2×10^30^ kg; mass of mars = 6.4×10^23^ kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28×10^8^ km; G = 6.67×10^-11^ Nm^2^kg^-2^. **Geostationary and polar satellites** **1 MARKS QUESTIONS** 142. Write the value of the time period of a geostationary satellite in its orbital around the earth. 143. Where should a geostationary satellite be launched? 144. What is the height of the geostationary satellite? **2 MARKS QUESTIONS** 145. Obtain a formula for the orbital radius, R~G~, of a geostationary satellite in terms of 'T' -- the time duration of the earth's day. 146. What are the necessary conditions for a satellite to appear stationary? **5 MARKS QUESTIONS** 147. \(a) A geostationary satellite is orbiting at a height of 6R above the surface of earth; R being the radius of the earth. What will be the time period of revolution of another satellite at a height of 2.5 R from the surface of earth? \(b) Give some use of geostationary satellites. 148. What are geostationary satellites? Calculate the height of the orbit above the surface of the earth in which a satellite, if placed will appear stationary. State the necessary conditions for a satellite to be geostationary. **Weightlessness** **1 MARKS QUESTIONS** 149. Can we determine the gravitational mass of body inside an artificial satellite? 150. Why does an astronaut in space feel weightlessness? 151. Why does a person feels weightlessness in satellite? **2 MARKS QUESTIONS** 152. A person sitting in a satellite of earth feels weightlessness but a person standing on moon has weight though moon is also a satellite of earth. Why? 153. The astronauts in a satellite orbiting the earth feel weightlessness. Does the weightlessness depend upon the distance of the satellite from the earth? Give reason. **4 MARKS QUESTIONS** 154. Deepa and Shilpa were two students of class XI. Once they were discussing the law of gravitation with each other. Deepa asked Shilpa that a person sitting in a satellite feels weightlessness but a person standing on the moon has weight through moon is also a satellite of the earth. Both could not find suitable answer for this problem. They went to their physics teacher and sought answer for this question. The teacher explained the reason behind this nicely. a. What are the value being displayed by Deepa and shilpa? b. What can be the possible answer for their problem? 155. Sohan is a student of class XI and reads an article on astronomy in a magazine. Astronauts spend weeks and months in orbiting spacecrafts and space stations. Although gravity acts on them, the astronauts experience ling distance of zero gravity due to centripetal motion. On earth, gravity provides the force that causes our muscles and bones to develop top the proper strength so that we may function in our environment. After reading the article some questions arise in his mind. He goes to his physics teacher to know the answer. Answer the following questions based on the information. a. What happens to muscles and bones in a zero gravity environment? b. How is our circulatory system affected? c. Do astronauts lose blood in zero gravity environments? d. What inference do you draw from the above discussion?