Chapter 21: Problem 9
Two spheres \(P\) and \(Q\) of equal radii have densities \(\rho_{1}\) and \(\rho_{2}\), respectively. The spheres are connected by a massless string and placed in liquids \(L_{1}\) and \(L_{2}\) of densities \(\sigma_{1}\) and \(\sigma_{2}\) and viscosities \(\eta_{1}\) and \(\eta_{2}\), respectively. They float in equilibrium with the sphere \(P\) in \(L_{1}\) and sphere \(Q\) in \(L_{2}\) and the string being taut (see figure). If sphere \(P\) alone in \(L_{2}\) has terminal velocity \(\vec{V}_{P}\) and \(Q\) alone in \(L_{1}\) has terminal velocity \(\vec{V}_{Q}\), then(A) \(\frac{\left|\vec{V}_{P}\right|}{\left|\vec{V}_{Q}\right|}=\frac{\eta_{1}}{\eta_{2}}\) (B) \(\frac{\left|\vec{V}_{P}\right|}{\left|\vec{V}_{Q}\right|}=\frac{\eta_{2}}{\eta_{1}}\) (C) \(\vec{V}_{P} \cdot \vec{V}_{Q}>0\) (D) \(\quad \vec{V}_{P} \cdot \vec{V}_{Q}<0\)
Short Answer
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