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Question

# A particle is thrown vertically upwards with velocity 11.2kms−1 from the surface of earth. Calculate its velocity at height 3R, where R is the radius of earth.

A
9.25 kms1
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B
5.6 kms1
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C
11.2 kms1
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D
4.3 kms1
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Solution

## The correct option is B ≃ 5.6 kms−1The given velocity equals escape velocity.So, GMmR= initial K.Evescape=√2GMRInitial total energy =K.E+P.E=−GMmR+GMmR=0So, at height 3R which is equal to distance 4R from the centre of the earth, total energy will be zero.Hence,0=−GMm4R+12mv2⇒v=√GM2R=vescape2On solving, we get v=5.6m/s

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