The ratio of acceleration due to gravity at a height 3 R above earth's surface to the acceleration due to gravity on the surface of the earth is ( R = radius of earth)

Question

The ratio of acceleration due to gravity at a height 3 R above earth's surface to the acceleration due to gravity on the surface of the earth is ( R = radius of earth), 1 9, 1 4, 1 16, 1 3

MARKS App · Accepted Answer

The value of acceleration due to gravity changes with height ( i e , a l t i t u d e ) . If g ′ is the acceleration due to gravity at a point, at height h above the surface of earth, then g ′ = G M R + h 2 b u t , g = G M R 2 ∴ g ′ g = G M R + h 2 × R 2 G M = R 2 R + h 2 H e r e , g ′ = G M R + h 2 = G M R + 3 R 2 = G M 4 R 2 = G M 16 R 2 = g e 16

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