A metal sphere of radius R and density rho_1 | vedclass

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Question

(A) The terminal velocity $V_T$ of a sphere of radius $R$ and density $\rho$ falling through a liquid of density $\sigma$ and viscosity $\eta$ is give

Vedclass · Accepted Answer

$V \left[ (\rho_2 - \sigma) / (\rho_1 - \sigma) \right]$

Vedclass · Answer

(A) The terminal velocity $V_T$ of a sphere of radius $R$ and density $\rho$ falling through a liquid of density $\sigma$ and viscosity $\eta$ is given by Stokes' Law: $V_T = \frac{2}{9} \frac{R^2 (\rho - \sigma) g}{\eta}$ Since $R$,$g$,and $\eta$ are constant for both spheres,the terminal velocity is directly proportional to the difference in densities: $V \propto (\rho - \sigma)$ Therefore,for the first sphere: $V \propto (\rho_1 - \sigma)$ For the second sphere with terminal velocity $V'$: $V' \propto (\rho_2 - \sigma)$ Taking the ratio: $\frac{V'}{V} = \frac{\rho_2 - \sigma}{\rho_1 - \sigma}$ $V' = V \left[ \frac{\rho_2 - \sigma}{\rho_1 - \sigma} \right]$

$A$ metal sphere of radius $R$ and density $\rho_1$ is dropped in a liquid of density $\sigma$ and moves with terminal velocity $V$. Another metal sphere of the same radius and density $\rho_2$ is dropped in the same liquid. Its terminal velocity will be:

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