07%20-%20Gravitation

# 07%20-%20Gravitation - 7 - GRAVITATION Page 1 ( Answers at...

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- GRAVITATION Page 1 ( Answers at the end of all questions ) 1 ) The change in the value of ‘g’ at a height ‘h’ above the surface of the earth is the same as at a depth ‘d’ below the surface of earth. When both ‘d’ and ‘h’ are much smaller than the radius of the earth, then which one of the following is correct ? ( a ) d = 3h / 2 ( b ) d = h / 2 ( c ) d = h ( d ) d = 2h [ AIEEE 2005, 2003 ] 2 ) A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle far away from the surface. ( G = 6.67 × 10 - 11 Nm 2 / kg 2 ) ( a ) 3.33 × 10 - 10 J ( b ) 13.34 × 10 - 10 J ( c ) 6.67 × 10 - 10 J ( d ) 6.67 × 10 - 9 J [ AIEEE 2005 ] 3 ) Average density of the earth ( a ) is a complex function of g ( b ) does not depend on g ( c ) is inversely proportional to g ( d ) is directly proportional to g [ AIEEE 2005 ] 4 ) A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is ( a ) gx ( b ) gR / ( R - x ) ( c ) gR 2 /( R + x ) ( d ) [ gR 2 /( R + x ) ] 1 / 2 [ AIEEE 2004 ] 5 ) The time-period of an earth satellite in circular orbit is independent of ( a ) the mass of the satellite ( b ) radius of its orbit ( c ) both the mass and radius of the orbit ( d ) neither the mass of the satellite nor the radius of its orbit [ AIEEE 2004 ] 6 ) If g is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is ( a ) 2 mgR ( b ) ( 1 / 2 ) mgR ( c ) ( 1 / 4 ) mgR ( d ) mgR [ AIEEE 2004, IIT 1983 ] 7 ) Suppose the gravitational force varies inversely as the nth power of the distance. Then the time-period of a planet in circular orbit of radius R around the sun will be proportional to ( a ) R ( n + 1 ) / 2 ( b ) R ( n - 1 ) / 2 ( c ) R n ( d ) R ( n - 2 ) / 2 [ AIEEE 2004 ] 8 ) The time-period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time-period will become ( a ) 10 hours ( b ) 20 hours ( c ) 40 hours ( d ) 80 hours [ AIEEE 2003 ] 9 ) The escape velocity for a body projected vertically upwards from the surface of the earth is 11 km / s. If the body is projected at an angle of 45 ° with the vertical, the escape velocity will be ( a ) 11 / √ 2 km / s ( b ) 11 2 km / s ( c ) 2 km / s ( d ) 11 km / s [ AIEEE 2003 ] 10 ) A body weighs 500 N on the surface of the earth. How much would it weigh half way below the surface of the earth ? ( a )

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## This note was uploaded on 11/28/2011 for the course PHYSICS 300 taught by Professor Smith during the Spring '06 term at ITT Tech Flint.

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07%20-%20Gravitation - 7 - GRAVITATION Page 1 ( Answers at...

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