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/2`
B. `R/3`
C. `R/4`
D. `R/5`

Answer

B

Explanation

` -(GMm)/R + 1/2(mV^2/4 )-(gMm)/R+h`
`[therefore V_e=sqrt2G]`
`(2GM)/(8R)=(GMh)/R(R+h)`
`Rightarrow 1/4= (h)/(R+h)`
`Rightarrow R+h= 4h`
`therefore h= R/3`