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

• A. $4 \pi G / 3 g R$
• B. $3 \pi R / 4 g G$
• C. $3 g / 4 \pi R G$
• D. $\pi R G / 12 G$

Answer 1

Answer: (C)

$3 g / 4 \pi R G$

Answer 2

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

$\therefore g = \frac { 4 } { 3 } \frac { \pi R ^ { 3 } \times G \rho } { R ^ { 2 } } \Rightarrow \rho = \frac { 3 g . } { 4 \pi R G }$