(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

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

(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: $\frac{V'}{V} = \frac{\rho_2 - \sigma}{\rho_1 - \sigma}$ $V' = V \left[ \frac{\rho_2 - \sigma}{\rho_1 - \sigma} \right]$

Class 11 Physics Fluid Mechanics and Surface Tension Viscosity and Stoke's Law and Terminal Velocity

Medium

$A$ 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:

MHT CET 2019 All MHT CET

A
$V \left[ (\rho_2 - \sigma) / (\rho_1 - \sigma) \right]$
B
$V \left[ (\rho_1 - \sigma) / (\rho_2 - \sigma) \right]$
C
$V \left[ (\rho_2 + \sigma) / (\rho_1 + \sigma) \right]$
D
$V \left[ (\rho_1 + \sigma) / (\rho_2 + \sigma) \right]$

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Viscosity and Stoke's Law and Terminal Velocity

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$A$ 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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$A$ stone is projected vertically up from the bottom of a water tank. Assuming no water resistance,it will go up and come down in the same time. However,if water drag (resistance) is present,then the time it takes to go up,$t_{up}$,and the time it takes to come down,$t_{down}$,are related as:

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