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Question

An object of mass m is at rest on earth's surface. Escape speed of this object is ve. Same object is orbiting earth with h=R, then its escape speed will be ve. Find the correct alternative

A
ve=ve4
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B
ve=2ve
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C
ve =ve2
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D
ve=2ve3
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Solution

The correct option is C ve =ve2

The escape velocity for an object at a distance r from the center of the Earth
ve=2GMrOn the surface of earth, r=R

ve=2GMR....(1)

At the altitude R from earth surface, r=R+R=2R

ve=2GM2R....(2)

From equation (1) and (2),

ve=ve2

Hence, option (c) is the correct answer.

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