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] $
Show Answer
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}] $
