If the terminal speed of a sphere A [density | vedclass

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(B) The terminal velocity $V$ of a sphere of radius $r$ and density $\rho$ falling through a liquid of density $\rho_L$ and viscosity $\eta$ is given

Vedclass · Accepted Answer

$0.1$

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(B) The terminal velocity $V$ of a sphere of radius $r$ and density $\rho$ falling through a liquid of density $\rho_L$ and viscosity $\eta$ is given by the formula:$V = \frac{2}{9} \frac{r^2 g (\rho - \rho_L)}{\eta}$Since the spheres have the same size ($r$ is constant) and are in the same liquid ($\eta$ and $\rho_L$ are constant),the terminal velocity is directly proportional to the difference in densities:$V \propto (\rho - \rho_L)$Therefore,the ratio of the terminal velocities is:$\frac{V_A}{V_B} = \frac{\rho_A - \rho_L}{\rho_B - \rho_L}$Substituting the given values:$\frac{0.4}{V_B} = \frac{7.5 - 1.5}{3 - 1.5} = \frac{6.0}{1.5} = 4$$V_B = \frac{0.4}{4} = 0.1 \ ms^{-1}$

If the terminal speed of a sphere $A$ [density $\rho_A = 7.5 \ kg \ m^{-3}$] is $0.4 \ ms^{-1}$ in a viscous liquid [density $\rho_L = 1.5 \ kg \ m^{-3}$],the terminal speed of sphere $B$ [density $\rho_B = 3 \ kg \ m^{-3}$] of the same size in the same liquid is: (in $ms^{-1}$)

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