A metal sphere of radius R,density rho_1 move | vedclass

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Question

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

Vedclass · Accepted Answer

$(\rho_1 - \sigma) : (\rho_2 - \sigma)$

Vedclass · Answer

(A) The terminal velocity $v$ of a sphere of radius $R$ and density $\rho$ falling through a liquid of density $\sigma$ and viscosity $\eta$ is given by Stokes' Law as:$v = \frac{2}{9} \frac{(\rho - \sigma) R^2 g}{\eta}$For the first sphere with density $\rho_1$ and terminal velocity $V_1$:$V_1 = \frac{2}{9} \frac{(\rho_1 - \sigma) R^2 g}{\eta}$For the second sphere with density $\rho_2$ and terminal velocity $V_2$:$V_2 = \frac{2}{9} \frac{(\rho_2 - \sigma) R^2 g}{\eta}$Taking the ratio of $V_1$ to $V_2$:$\frac{V_1}{V_2} = \frac{\frac{2}{9} \frac{(\rho_1 - \sigma) R^2 g}{\eta}}{\frac{2}{9} \frac{(\rho_2 - \sigma) R^2 g}{\eta}}$$\frac{V_1}{V_2} = \frac{\rho_1 - \sigma}{\rho_2 - \sigma}$Therefore,the ratio $V_1 : V_2$ is $(\rho_1 - \sigma) : (\rho_2 - \sigma)$.

$A$ metal sphere of radius $R$,density $\rho_1$ moves with terminal velocity $V_1$ through a liquid of density $\sigma$. Another sphere of same radius but density $\rho_2$ moves through the same liquid. Its terminal velocity is $V_2$. The ratio $V_1: V_2$ is

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