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Question

# If the satellite is stopped suddenly in its orbit whichis at a distance radius of earth from earth's surface and allowed to fall freely into the earth. The speed with which it hits the surface of earth will be.

A
1. 7.919m/s
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B
7.919km/s
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C
11.2m/s
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D
11.2km/s
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Solution

## The correct option is A 7.919km/sAt h=R, K.E is zero as satellite is stopped suddenly. T.Eh=0+(−GMm2R) (r=h+R=2R)At the surface of earth, let velocity attained be v.T.Es=12mv2+(−GMmR)Apply conservation of energy at h and surface of earth-−GMm2R=12mv2−GMmR⟹v=√GMRv=√gR (using GM=gR2)v=√9.8×6400×1000⟹v=7.919km/s

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