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On the surface of earth, the escape velo...

On the surface of earth, the escape velocity of a body is `11.2 km//s`. If mass of earth is made half and radius becomes twice, then the escape velocity will become

A

5.6 km/s

B

22.4 km/s

C

33.4 km/s

D

11.2 km/s

Text Solution

Verified by Experts

The correct Answer is:
A
`V_(e)` = Initial escape velocity `= sqrt((2GM)/(R ))`
`V_(e) = 11.2 km//s`
`V_(e)` = Final escape velocity
`= sqrt((2GM)/(2(2R))) = sqrt((1)/(4)(2GM)/(R ))`
`V._(e) = (1)/(2)V_(e)`
= 5.6 km/s
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