Question

When the value of acceleration due to gravity 'g' becomes `(g/3)` above the earth's surface at height 'h' then relation between 'h' and 'R' is ______.

R =radius of the earth

Options

• `h=R(sqrt3-1)`

• `h=R(sqrt2-1)`

• h = 2R

• h = R

Answer 1

When the value of acceleration due to gravity 'g' becomes `(g/3)` above the earth's surface at height 'h' then relation between 'h' and 'R' is `underline(h=R(sqrt3-1))`.

Explanation:

`g/3=(GM)/(R+h)^2`           `g=(GM)/R^2`

`therefore g/3(R+h)^2=gR^2`

(R + h)² = 3R²

`R +h=sqrt3R`

`therefore h=sqrt3R-R=(sqrt3-1)R`