A body of mass m is projected from the Earth's surface. At the point of launch, the acceleration of free fall is g and the radius of the Earth is R. To escape from the gravitational field of the Earth, the speed of the body must be at least:
Correct answer: A. √(gR)
- A. √(gR)
- B. mgR
- C. √(2gR)
- D. mg/2R
Explanation
a) √(gR):This option suggests that the speed of the body must be at least √(gR) to escape from the gravitational field of the Earth. This is the correct option. The escape speed from the Earth's gravitational field can be calculated using the formula √(2gR), which takes into account the acceleration due to gravity (g) and the radius of the Earth (R). So, this option represents the correct relationship between g and R.
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About Satellite Motion and Orbital Velocity
Satellite motion uses gravitational force as the centripetal force required for circular orbit, giving relationships among orbital radius, period and orbital velocity. Questions cover geostationary conditions and weightlessness, while distinguishing orbital velocity, escape velocity and the satellite's tangential speed.
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