At what distance above and below the surface of the earth a body will have same weight, (take radius of earth as R.)
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At what distance above and below the surface of the earth a body will have same weight, (take radius of earth as R.)

G1 Physics · Accepted Answer

At height h above the surface, g(p) = gR²/(R + h)² At depth h below the surface, g(q) = g(1 - h/R) For same weight, g(p) = g(q) R²/(R + h)² = 1 - h/R Let, x = h/R Then, 1/(1 + x)² = 1 - x ⇒ (1 - x)(1 + x)² = 1 ⇒ x³ + x² - x = 0 Ignoring x = 0, x² + x - 1 = 0 x = (√5 - 1)/2 Therefore, h = R(√5 - 1)/2