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Question

A particle of mass m is dropped from a height 2R from the surface of the earth. The speed with which the particle hits the surface of the earth is:

A
2gR3
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B
2gR
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C
4gR3
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D
2gR5
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Solution

The correct option is A 2gR3
Applying energy conservation principle between the topmost point and the surface of earth, we have:

Loss in potential energy of the system = Increase in kinetic energy of the particle.

ΔU=ΔKE

mgh1+hR=12mv2

mg(2R)1+2RR=12mv2

v=2gR3

Hence, option (A) is the correct answer.


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