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A body stretches a spring by a particular length at the earth’s surface at equator. At what height above the south pole will it stretch the same spring by the same length? Assume the earth to be spherical.

A body stretches a spring by a particular length at the earth’s surface at equator. At what height above the south pole will it stretch the same spring by the same length? Assume the earth to be spherical.

Grade:10

1 Answers

Deepak Patra
askIITians Faculty 471 Points
7 years ago
Sol. At equator, g’ = g – ω^2R …(1) Let at ‘h’ height above the south pole, the acceleration due to gravity is same. Then, here g’ = g (1 – 2h/R) …(2) ∴ g - ω^2 R = g (1 – 2h/R) or 1 - ω^2R/g = 1 2h/R or h = ω^2R^2/2g = (7.3 * 10^-5)^2 * (6400 * 10^3)^2/2 * 9.81 = 11125 N = 10Km (approximately)

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