If the potential energy of body on a planet is numerically U and the escape velocity for the same body is `v_(e )` for same planet then `(U)/(v_(e ))` will be :

Options

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

Answer

A

Explanation

Potential energy of body
`U=(GMm)/(R ) " " ` (numerically)
Escape velocity is `v_(e )=sqrt((2GM)/(R )) `
`therefore (U)/(v_(e ))=(GMm)/(R ) xx sqrt((R )/(2GM))`
`therefore (U)/(v_(e )) =m sqrt((GM)/(2R))`.
Thus correct choice is (a).