The acceleration due to gravity becomes (g/2) where g=acceleration due to gravity

The Acceleration Due To Gravity Becomes G2 Where Gacceleration Due Physics QuestionThe Acceleration Due To Gravity Becomes G2 Where Gacceleration Due Physics Question

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

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