Question

A body is projected vertically upwards from earth's surface. If velocity of projection is `(1/3)^"rd"` of escape velocity, then the height upto which a body rises is ______.

(R =radius of earth)

Options

• `R/4`

• 2R

• R

• `R/8`

Answer 1

A body is projected vertically upwards from earth's surface. If velocity of projection is `(1/3)^"rd"` of escape velocity, then the height upto which a body rises is `underline(R/8)`.

Explanation:

`V=1/3sqrt("2GM"/R)`

TE_{At surface} = TE_{at height h}

`-"GMm"/R+1/2"mv"^2=-"GMm"/(R+h)+0`

`-"GMm"/R+1/2m1/9xx"2GM"/R=-"GMm"/(R+h)`

`(1/9-1)"GMm"/R=-"GMm"/(R+h)`

`-8/9"GMm"/R=-"GMm"/(R+h)`

`8/9 1/R=1/(R+h)`

⇒ 8R + 8h = 9R

8h = R

`thereforeh=R/8`