A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is :

Options

A. `(R )/(3)`
B. `(R )/(2)`
C. `(2R)/(3)`
D. `(5R)/(3)`.

Answer

A

Explanation

Let the body reaches at a height h above the surface of earth.
`therefore -(GMm)/(R+h)+0= -(GMm)/(R )+(1)/(2)m [(1)/(2) sqrt((2GM)/(R ))]^(2)`
`-(GMm)/(R+h)= -(GMm)/(R )+(1)/(2)m[(1)/(4)(2GM)/(R )]`
`-(GMm)/(R+h)= -(GMm)/(R )+(1)/(4)(GMm)/(R )= -(3)/(4)(GMm)/(R )`
`(1)/(R+h)=(3)/(4R) rArr 3R+3h = GR rArr h=R//3`.
Hence the correct choice is (a).