Book Online Demo

Check Your IQ

Try Test

Courses

What is the average density of the earth in terms of $g, G,$ and $R$ .

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

\frac{4 g}{3 GR}

\frac{3 g}{4 GR}

\frac{3 G}{4 gR}

None of the above

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The average density of the earth in terms of

g, G,

and

R

\frac{3 g}{4 GR}

.
Assume

M

is the mass of earth and

R

is the radius of the earth. So the volume of the earth is

\frac{4}{3} π R^{3}

.
Therefore the density of the earth is

\Rightarrow ρ = \frac{Mass}{Volume}

\Rightarrow ρ = \frac{M}{\frac{4}{3} π R^{3}}

Now acceleration due to gravity

g = \frac{GM}{R^{2}}

or,

M = \frac{g R^{2}}{G}

.
Substituting this value of M in above we get,

\Rightarrow ρ = \frac{\frac{g R^{2}}{G}}{\frac{4}{3} π R^{3}}

\Rightarrow ρ = \frac{3 g}{4 GR}

Watch 3-min video & get full concept clarity