Two similar spheres of the same material have masses of 12kg and250kg respectively. find the radius of the smaller sphere if the radius of the bigger shere is 12.5cm


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Question Number 55918 by imamu222 last updated on 06/Mar/19

$T w o s i m i l a r s p h e r e s o f t h e s a m e m a t e r i a l h a v e m a s s e s o f 12 k g a n d 250 k g r e s p e c t i v e l y . f i n d t h e r a d i u s o f t h e s m a l l e r s p h e r e i f t h e r a d i u s o f t h e b i g g e r s h e r e i s 12.5 c m$
	Answered by tanmay.chaudhury50@gmail.com last updated on 06/Mar/19

	$\frac{M_{s m a l l}}{M_{l a r g e}} = \frac{\frac{4}{3} π r_{s m a l l}^{3} ρ}{\frac{4}{3} π r_{l a r g e}^{3} ρ}$ $\frac{M_{s}}{M_{l}} = \frac{r_{s}^{3}}{r_{l}^{3}} \to r_{s}^{3} = r_{l}^{3} (\frac{M_{s}}{M_{l}})$ $r_{s} = r_{l} {(\frac{M_{s}}{M_{l}})}^{\frac{1}{3}} \to r_{s} = 12.5 {(\frac{12}{250})}^{\frac{1}{3}} \approx 4.5428 c m$
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