A body is projected vertically from the surface of the earth of radius 'R' with a velocity equal t half of the escape velocity . The maximum heign reached by the body is

Options

A. `R/6`
B. `R/3`
C. `2R3`
D. R

Answer

B

Explanation

maximum height attained by an object is given by,
h= `(v^2R)(v^2R)/(2gR-V^2)`
Velocity of body = Half the escape velocity
v=`(v_e)/2 =(sqrt2gr)/2`
`v^2= (gR)/2`
h= `((gR)/2. R)/(2gR-(gR)/2)= ((gR)^2/2)/((4gR-gr)/2)=R/3`