The mass density of a spherical body is given | vedclass

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Question

Give that, mass desity $\left( {\frac{{mass}}{{volume}}} \right)$ of a 

spherical body $\rho \left( r \right) = \frac{k}{r}$

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Vedclass · Accepted Answer

Vedclass · Answer

Give that, mass desity $\left( {\frac{{mass}}{{volume}}} \right)$ of a 

spherical body $\rho \left( r \right) = \frac{k}{r}$

$\frac{M}{V} = \frac{k}{r}\,for\,inside\,r \le R$

$M = \frac{{kv}}{r}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)$

Inside the surface of sphere Intensity

$I = \frac{{GMr}}{{{R^3}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,I = \frac{F}{m}$

${g_{inside}} = \frac{{GMr}}{{{R^3}}}\,\,\,\,\,\,\,\,\,\,\,or\,\,\,\,\,\,\,\,\,\,I = \frac{{mg}}{m} = g$

$ = \frac{G}{{{R^3}}}\frac{{kv}}{r}.r = constant\,\,\,\,\,From\,eq.\,\left( i \right),$

$similarly,\,{g_{out}} = \frac{{GM}}{{{r^2}}}$

Hence, option $(b)$ is correct graph.

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