If the terminal speed of a sphere of gold (de | vedclass

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(C) 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

$0.1$

Vedclass · Answer

(C) The terminal velocity $V_T$ of a sphere of radius $r$ and density $ho$ falling through a liquid of density $\sigma$ and viscosity $\eta$ is given by $V_T = \frac{2r^2}{9\eta}(ho - \sigma)g$.Since $r$,$\eta$,and $\sigma$ are the same for both spheres,$V_T \propto (ho - \sigma)$.For gold: $V_{T1} = 0.2 \, m/s$,$ho_1 = 19.5 	imes 10^3 \, kg/m^3$,$\sigma = 1.5 	imes 10^3 \, kg/m^3$.$V_{T1} \propto (19.5 - 1.5) = 18$.For silver: $V_{T2} = ?$,$ho_2 = 10.5 	imes 10^3 \, kg/m^3$.$V_{T2} \propto (10.5 - 1.5) = 9$.Taking the ratio: $\frac{V_{T2}}{V_{T1}} = \frac{9}{18} = 0.5$.$V_{T2} = 0.5 	imes V_{T1} = 0.5 	imes 0.2 = 0.1 \, m/s$.

If the terminal speed of a sphere of gold (density $= 19.5 \times 10^3 \, kg/m^3$) is $0.2 \, m/s$ in a viscous liquid (density $= 1.5 \times 10^3 \, kg/m^3$),find the terminal speed of a sphere of silver (density $= 10.5 \times 10^3 \, kg/m^3$) of the same size in the same liquid.

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