A planet is moving in a circular orbit around earth. Then the minimum increase of its orbital speed for which the planet will escape to infinity is _____
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a
26.3 %
b
41.4 %
c
50 %
d
73.2 %
answer is B.
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Detailed Solution
New orbital speed must be equal to the magnitude of escape velocity at any position of the orbit.V=GMr, V'=2GMr =2V∴ % increase=V'−VV=2−1 × 100%=41.4%