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If a rocket is fired with a velocity, V=...

If a rocket is fired with a velocity, `V=2sqrt(gR)` near the earth's surface and goes upwards, its speed in the inter-stellar space is

A

`4 sqrt(gR)`

B

`sqrt(2gR)`

C

`sqrt(gR)`

D

`sqrt(4gR)`

Text Solution

Verified by Experts

The correct Answer is:
B
Applying law of conservation of energy,
`(1)/(2)mv^(2) -(GMm)/(R) = (1)/(2)mv_(1)^(2) +0`
or `(1)/(2)mv_(1)^(2) =(1)/(2)mv^(2) -(GMm)/(R)`
or `v_(1)^(2) = v^(2)-(2GM)/(R) = v^(2)-v_(e)^(2)`
`:. v_(1) = sqrt(v^(2)-v_(e)^(2))`
`= sqrt(4gR-2gR)`
`= sqrt(2gR)`
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