Two spheres of different material are falling | vedclass

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Question

(C) The terminal velocity $v_t$ of a sphere of radius $r$ and density $\rho$ falling through a liquid of density $\rho_L$ and viscosity $\eta$ is give

Vedclass · Accepted Answer

$\sqrt{3/2}$

Vedclass · Answer

(C) The terminal velocity $v_t$ of a sphere of radius $r$ and density $ho$ falling through a liquid of density $ho_L$ and viscosity $\eta$ is given by Stokes' Law: $v_t = \frac{2}{9} \frac{r^2 g}{\eta} (ho - ho_L)$.Since both spheres fall with the same uniform terminal speed $v_t$,we have: $r_1^2 (ho_1 - ho_L) = r_2^2 (ho_2 - ho_L)$.Rearranging for the ratio of radii: $\frac{r_1^2}{r_2^2} = \frac{ho_2 - ho_L}{ho_1 - ho_L}$.Substituting the given values: $\frac{r_1^2}{r_2^2} = \frac{11 	imes 10^3 - 2 	imes 10^3}{8 	imes 10^3 - 2 	imes 10^3} = \frac{9 	imes 10^3}{6 	imes 10^3} = \frac{9}{6} = \frac{3}{2}$.Therefore,the ratio of their radii is $\frac{r_1}{r_2} = \sqrt{\frac{3}{2}}$.

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