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

`(h)/(R)=(u^(2))/(v_(e)^(2)-u^(2))=((1)/(4)v_(e)^(2))/(v_(e)^(2)-(1)/(4)v_(e)^(2))=((1)/(4)v_(e)^(2))/((3)/(4)v_(e)^(2))=(1)/(3)`
`h=(R)/(3)`