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Question

# if the radius of the earth shrinks by 0.2% without any charge in its mass, the escape velocity from the surface of the earth

A
Increases by 0.2%
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B
decreases by 2.02%
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C
Increases by 1.01%
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D
decreases by 0.4%
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Solution

## The correct option is C Increases by 1.01%Given that, Mass of earth = M Radius of earth = R We know that, The escape velocity is v=√2GMR Now, the radius R′=R−R0.2 R′=R−R20 R′=0.98R Now, the escape velocity is v′=√2GM0.98R v′=1.0101√2GMR Now, the change in escape velocity =v′−v =1.0101√2GMR−√2GMR =(1.0101−1)√GMR v′−vv×100=1.01% Hence, the escape velocity is increases by 1.01%

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