Read the paragraph and answer the following questions.
Paragraph : Orbital velocity is defined as the velocity required to put the satellite into satellite into its orbit around the earth. An artificial satellite is moving in circular orbit around the earth with speed equal to half the value of escape velocity from the earth.
If the satellite is stopped suddenly in its orbit and allowed to fall freely on the surface of earth then the speed with which it hits the surface of earth is

Options

A. `sqrt((gR)/(g))`
B. `sqrt(gR)`
C. `sqrt(2gR)`
D. `sqrt(3gR)`

Answer

B

Explanation

Gain in K.E. = loss of P.E.
`(1)/(2)mv^(2)= (-GMm)/(2R)-[(-GMm)/(R )]`
`=(-GMm+2GMm)/(2R)=(GMm)/(2R)`
`v=sqrt((GM)/(R ))=sqrt(gR)`. So correct choice is b.