Question

# Escape velocity for a projectile at earth's surface is Ve. A body is projected from earth's surface with a velocity 2Ve. The velocity of the body when it is at infinite distance from the center of the earth is?

A
Ve
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B
2Ve
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C
2Ve
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D
3Ve
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Solution

## The correct option is D √3Ve Let v be the speed of the body when it is at infinite distance from the center of the earth and u be speed of projection of the body from the earth's surface. According to law of conservation of mechanical energy, 12mu2−GMmR=12mv2−0 v2=u2−2GMR v2=u2−Ve2(∵Ve=√2GMR) Given that u=2Ve So, v=√(2Ve)2−V2e=√3Ve

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