With what velocity should a particle be projected so that its height becomes equal to radius of earth?

Options

A. `((GM)/R)^(1//2)`
B. `((8GM)/R)^(1//2)`
C. `((2GM)/R)^(1//2)`
D. `((4GM)/R)^(1//2)`

Answer

A

Explanation

Apply energy conservation `"-GMm"/R+1/2mv^2`
`=-"GMm"/"2R" rArr v=sqrt((GM)/R)`