A metal sphere of mass m and density sigma_1 | vedclass

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(C) Given: Mass of sphere $= m$,Density of sphere $= \sigma_1$,Density of liquid $= \sigma_2$.At terminal velocity $v_t$,the forces acting on the sphe

Vedclass · Accepted Answer

$m g\left(1-\frac{\sigma_2}{\sigma_1}\right)$

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(C) Given: Mass of sphere $= m$,Density of sphere $= \sigma_1$,Density of liquid $= \sigma_2$.At terminal velocity $v_t$,the forces acting on the sphere are balanced.The downward force is the weight $W = mg$.The upward forces are the viscous force $F_V$ and the buoyant force $F_B$.$W = F_V + F_B$$mg = F_V + (	ext{Volume} 	imes \sigma_2 	imes g)$Since $m = \sigma_1 	imes 	ext{Volume}$,we have $	ext{Volume} = \frac{m}{\sigma_1}$.$mg = F_V + \left(\frac{m}{\sigma_1} 	imes \sigma_2 	imes gight)$$F_V = mg - \frac{m \sigma_2 g}{\sigma_1}$$F_V = mg \left(1 - \frac{\sigma_2}{\sigma_1}ight)$

$A$ metal sphere of mass $m$ and density $\sigma_1$ falls with terminal velocity through a container containing liquid. The density of the liquid is $\sigma_2$. The viscous force acting on the sphere is:

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