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

Applying conservation of mechanical energy,
`(1)/(2)m((v_(e))/(2))^(2)=(mgh)/(1+(h)/(R))or(v_(e)^(2))/(8)=(gh)/(1+(h)/(R))`
or `(2gR)/(8)=(gh)/(1+h//R)`....(i) `(because v_(e) = sqrt(2gR))`
On solving Eq. (i), we get `h= (R)/(3)`.