A body attains a height equal to the radius of the earth. The velocity of the body with which it was projected is

Options

A. `sqrt((GM)/(R))`
B. `sqrt((2GM)/(R))`
C. `sqrt((1)/(4)(GM)/(R))`
D. `sqrt((GM)/(2R))`

Answer

A

Explanation

Applying conservation of mechanical energy we get,
`(1)/(2)mv^(2)=(mgh)/(1+h//R)`
Putting h = R, we get
`v=sqrt(gR)=sqrt((GM)/(R))`