Which of the following is the variation of acceleration due to gravity at a depth “d” below the earth’s surface? Let “R” be the radius of the earth and “M1” the mass of earth. (Assume the density of the earth to be constant) /d c) g = (G x M1/R3) / (R – d) d) g = (G x M1/R3) x (R – d)

Which of the following is the variation of acceleration due to gravity at a depth “d” below the earth’s surface? Let “R” be the radius of the earth and “M1” the mass of earth. (Assume the density of the earth to be constant) /d c) g = (G x M1/R3) / (R – d) d) g = (G x M1/R3) x (R – d) Correct Answer

g = (G*M)/r2; M = Mass contained in an enclosed volume r = distance from centre of the earth to the depth “d” Therefore; r = R – d; where, R = Radius of the earth M = (density) x (volume) = (density) x = (density x 4 x pi x r3) / 3 = (M1 x r3) / R3 Therefore; g = (G x density x 4 x pi x r3) / (3 x r2) = (G x density x 4 x pi x r1) / 3 Therefore; g = x (R – d) = (G x M1/R3) x (R – d).
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