Gravitation Question 13

Question: If R is the radius of the earth and g the acceleration due to gravity on the earth’s surface, the mean density of the earth is [CPMT 1990; BHU 1998; Kerala PMT 2002; MH CET (Med.) 1999; CBSE PMT 1995]

Options:

A) $ [4\pi G/3gR] $

B) $ [3\pi R/4gG] $

C) $ [3g/4\pi RG] $

D) $ [\pi RG/12G] $

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Answer:

Correct Answer: C

Solution:

$ [g=\frac{GM}{R^{2}}] $ and $ [M=\frac{4}{3}\pi R^{3}\times \rho ] $

$ [\therefore ,,g=\frac{4}{3}\frac{\pi R^{3}\times GD}{R^{2}},\Rightarrow ,D=\frac{3g.}{4\pi RG}] $



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