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Question

# The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earth's mass increases to twice its present value and radius of the earth becomes half, the escape velocity from the new surface becomes

A
22.4 km/s
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B
44.8 km/s
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C
5.6 km/s
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D
11.2 km/s
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Solution

## The correct option is A 22.4 km/s As we know that the escape velocity near the surface of earth is given by Ve=√2GMR for new escape velocity, V′e=√2GM′R′ from question, M′=2M; R′=R/2 V′e=√2G(2M)(R/2)=2√2GMR ⇒V′e=2Ve=22.4 km/s Hence, option (a) is correct. Why this question ?To make students understand the dependence of escape velocity on mass and radius of a planet.

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