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With what angular velocity should the earth spin so that a body lying at 37° latitude becomes weightless?

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Important Questions on Gravitation

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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#1>Q 13
Which of the following graphs represent the time period of the planet moving around the sun? [R is semi-major axis of the path.]
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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#1>Q 14
The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is V0. The value of orbital velocity for another satellite orbiting at an altitude of half of earth's radius is,
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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#1>Q 15
If the distance between the earth and the sun were half its present value, then the number of days in a year would have been,
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KVPY Aptitude Test - Stream SX
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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#1>Q 16
A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.02R. The period of second satellite is larger than the first one by approximately,
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KVPY Aptitude Test - Stream SX
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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#1>Q 17
A satellite is moved from one circular orbit around the earth to another one of the lesser radius. Which of the following statements is true?
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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#1>Q 18
The mass of a spaceship is 1000 kg. It is to be launched from the earth's centre out into free space. The value of g and R (radius of earth) are 10 m s-2 and 6400 km, respectively. The required energy for this work will be,
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KVPY Aptitude Test - Stream SX
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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#2>Q 1
A satellite orbits around the earth at a distance r from the centre of the earth. Taking the zero of gravitational potential energy at infinity (KE and PE mean kinetic energy and potential energy respectively)
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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#2>Q 2

A body is projected horizontal on the top of the Mount Everest with speed much greater than 2gr, where r is the distance of the projection point from the centre of the earth and g is the acceleration due to gravity there. The trajectory of the body will be a