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

Options

A. `4sqrt(gR)`
B. `sqrt(2gR)`
C. `sqrt(gR)`
D. `sqrt(4gR)`

Answer

B

Explanation

According to the law of conservation of energy
`[T.E.]_("surface")=[T.E.]_("interstellarspace")`
`implies(-GMm)/R+1/2mv^(2)=0+1/2mv_(1)^(2)`
`impliesmgR+1/2m(2sqrt(gR))^(2)=1/2mv_(1)^(2)`
`implies1/2mv_(1)^(2)=mgRimpliesv_(1)^(2)=2gR=v_(1)=sqrt(2gR)`