A body is projected vertically upwards from the surface of the earth with a velocity equal to half of escape velocity of the earth. If `R` is radius of the earth, maximum height attained by the body from the surface of the earth is

Options

A. `(R )/(6)`
B. `(R )/(3)`
C. `(2R)/(3)`
D. R

Answer

B

Explanation

`1/2m(v_(e))/(2)^(2)=(mgh)/(R ) rarr 1/2m (2gR)/(4)=(mgR)/(R )`
`rarr 1/4=(1)/(1+(R )/(h)rarr 1+(R )/(h)=4 rarr(R )/(h)=3`
`therefore h=(R )/(3)`