The acceleration due to gravity becomes (g/2) where g=acceleration due to gravity on the surface of the earth at a height equal to

Options

(a) 4R
(b) R/4
(c) 2R
(d) R/2

Correct Answer:

R/4

Explanation:

Acceleration due to gravity g=GM/R² Acceleration due to gravity on the surface of the height is g’ = GM/(R+h)² .·. g/g’ = (GM/R²)/(GM/(R+h)²) = (R+h/R)² = (1+h/R)² g’/g = (1+h/R)⁻² = (1-2h/R), When h<<R (g/2)/g = (1-2h/R) ⇒ 1/2 = (1-2h/R) ⇒ 2h/R = 11/2 ⇒ 2h/R = 1/2 ⇒ h = (1/2)(R/2) = R/4