Question 311: Gravitation

Question

Two identical metal spheres are kept in contact with each other, each having radius ' $R$ ' cm and ' $\rho$ ' is the density of material of metal spheres. The gravitational force ' $F$ ' of attraction between them is proportional to

Accepted Answer

Force due to gravity,
$$\begin{aligned}
& \mathrm{F}=\frac{\mathrm{GMM}}{(2 \mathrm{R})^2} \
& \mathrm{~F}=\frac{\mathrm{GM}^2}{4 \mathrm{R}^2}\quad	ext{.... (i)}
\end{aligned}$$
Density, $ho=\frac{M}{V}$
$M=ho 	imes \frac{4}{3} \pi R^3$
Substituting in (i),
$$F=\frac{G\left(\frac{4}{3} \pi R^3 hoight)^2}{4 R^2}$$
$	herefore\quad F \propto R^4 ho^2$

Answer

$\mathrm{R}^3 \rho$

Answer

$R^4 \rho^2$

Answer

$R^4 \rho$

Answer

$\mathrm{R}^3 p^2$

Gravitation

Two identical metal spheres are kept in contact with each other, each having radius ' R ' cm and ' \rho ' is the density of material of metal spheres. The gravitational force ' F ' of attraction between them is proportional to

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