Question 308: Gravitation

Question

If ' $R$ ' is the radius of earth \& ' $g$ ' is acceleration due to gravity on earth's surface, then mean density of earth is

Accepted Answer

$$\begin{aligned}
&	ext { Mass of the Earth is given by, }\
&\mathrm{M}=\mathrm{V} ho=\frac{4}{3} \pi \mathrm{R}^3 ho\quad	ext{.... (i)}
\end{aligned}$$
Acceleration due to gravity is given by,
$$\mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^2}\quad	ext{.... (ii)}$$
Substituting equation (i) in equation (ii),
$$g=\frac{G}{R^2} 	imes \frac{4}{3} \pi R^3 ho \Rightarrow ho=\frac{3 g}{4 \pi R G}$$

Answer

$\frac{4 \pi G}{3 g R}$

Answer

$\frac{3 \pi R}{4 g G}$

Answer

$\frac{3 \mathrm{~g}}{4 \pi \mathrm{RG}}$

Answer

$\frac{\pi R G}{12 \mathrm{~g}}$

Gravitation

If ' R ' is the radius of earth \& ' g ' is acceleration due to gravity on earth's surface, then mean density of earth is

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