Question

Acceleration due to gravity 'g' in terms of mean density of the Earth 'd' and radius 'R' is:

(G is universal gravitational constant)

• A. 4​dG
• B.
• C.
• D. RdG

Answer 1

The correct option is D

RdG

The expression of 'g' on the Earth is, g = $\frac{GM}{R^2}$​

$M$ is mass of the Earth
We know density is, d = $\frac{M}{V}$
So, M = density $\times$ volume

volume = $\frac{4}{3}$$\pi$$R^3$​
M = d $\times$ $\frac{4}{3}$$\pi$$R^3$​​
By substituting these into the expression we obtain ‘g’ in terms of ‘d’ and G
$g=\frac{GM}{R^2}$

​​ $=G\times d\times \frac{\frac{4}{3}\pi R^3}{R^2}$

​$=\frac{4}{3}\pi RdG$