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The escape velocity from earth is v(es)....

The escape velocity from earth is `v_(es)`. A body is projected with velocity `2v_(es)` with what constant velocity will it move in the inter planetary space

A

`v_(B)`

B

`sqrt(2 ) v_(p)`

C

`sqrt(3) v_(r)`

D

`sqrt(5) v_(p)`

Text Solution

Verified by Experts

The correct Answer is:
C
`U_(s) + K_(i) = U_(f) + K_(f)`
`- (GM m)/(R) + (1)/(2) m (2v_(1))^(2) = 0 + (1)/(2) mv^(2)`
Or `- (GM)/(R) = 2v_(r)^(2) = (1)/(2) v^(2)`
Or `- (2G M)/(R) + (8 GM)/(R) = v^(2)`
Or ` v = sqrt((6GM)/( R)) = sqrt(3((2 GM)/(R)))`
`= sqrt(3 (2gR)) = sqrt(3) v_(e)`
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