A solid sphere of radius r made of a soft mat | vedclass

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Question

$Bulk\,modulus,\,K = \frac{{volumetric\,stress}}{{volumetric\,strain}}$

$K = \frac{{mg}}{{a\left( {\frac{{dV}}{V}} \right)}}\, \Rightarrow \frac{{d

Vedclass · Accepted Answer

$\frac{{mg}}{{3Ka}}$

Vedclass · Answer

$Bulk\,modulus,\,K = \frac{{volumetric\,stress}}{{volumetric\,strain}}$

$K = \frac{{mg}}{{a\left( {\frac{{dV}}{V}} ight)}}\, \Rightarrow \frac{{dV}}{V} = \frac{{mg}}{{Ka}}\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i ight)$

$Volume\,of\,sphere,\,V = \frac{4}{3}\pi {R^3}$

$Fractional\,change\,in\,volume\frac{{dV}}{V} = \frac{{3dr}}{r}\,\,\,\,\,...\left( {ii} ight)$

Using eq. $(i)$ & $(ii)$ $\frac{{3dr}}{r} = \frac{{mg}}{{Ka}}$

$	herefore \frac{{dr}}{r} = \frac{{mg}}{{3Ka}}\left( {fractional\,decrement\,in\,radius} ight)$

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