Question

$\huge\mathfrak {Question: }$



Calculate the average density of earth in terms of g , G and R.

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Answer 1

In this question, we are asked to find average density of earth in terms of g, G and R.

» g denotes acceleration due to gravity

» G denotes gravitational constant

» R denotes radius of earth

❖ Acceleration due to gravity of earth is given by

$\sf\longrightarrow\:g=\dfrac{GM}{R^2}$

where M denotes mass of the earth

$\sf\longrightarrow\:M=\dfrac{gR^2}{G}\:\dots\:(I)$

We know that density of object is defined as the ratio of mass to the volume.

Mathematically, $\underline{\boxed{\sf{\rho=\dfrac{M}{V}}}}$

• It is a scalar quantity having only magnitude.
• SI unit : kg/m³

We can assume earth as a solid sphere.

Hence volume = 4/3 πR³

From the 1st equation;

$\sf:\implies\:\rho=\dfrac{M}{V}$

$\sf:\implies\:\rho=\dfrac{gR^2}{G}\times\dfrac{3}{4\pi R^3}$

$\sf:\implies\:\rho=\dfrac{g}{G}\times\dfrac{3}{4\pi R}$

$:\implies\:\underline{\boxed{\bf{\orange{\rho=\dfrac{3g}{4\pi GR}}}}}$

Answer 2

The average density of the earth in terms of g,G and R is 3g4πGR.

Note: Acceleration due to gravity is the acceleration of a body falling freely under the influence of the Earth's gravitational pull at sea level. It is approximately equal to 9.8m/s2.

Tnxs for tnxs ;p