Properties Of Matter Ques 6
(a) $\frac{\left|\mathbf{v}_P\right|}{\left|\mathbf{v}_Q\right|}=\frac{\eta_1}{\eta_2}$
(b) $\frac{\left|\mathbf{v}_P\right|}{\left|\mathbf{v}_Q\right|}=\frac{\eta_2}{\eta_1}$
(c) $\mathbf{v}_P \cdot \mathbf{v}_Q>0$
(d) $\mathbf{v}_P \cdot \mathbf{v}_Q<0$
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Answer:
Correct Answer: 6.( a, d )
Solution:
- For floating, net weight of system $=$ net upthrust
$ \Rightarrow\left(\rho_1+\rho_2\right) V g=\left(\sigma_1+\sigma_2\right) V g $
Since string is taut, $\rho_1<\sigma_1$ and $\rho_2>\sigma_2$
$ \begin{aligned} \mathbf{v}_P & =\frac{2 r^2 g}{2 \eta_2}\left(\sigma_2-\rho_1\right) \quad \text { (upward terminal velocity) } \\ \mathbf{v}_Q & =\frac{2 r^2 g}{9 \eta_1}\left(\rho_2-\sigma_1\right) \text { (downward terminal velocity) } \\ \left|\frac{\mathbf{v}_P}{\mathbf{v}_Q}\right| & =\frac{\eta_1}{\eta_2} \end{aligned} $
Further, $\mathbf{v}_P \cdot \mathbf{v}_Q$ will be negative as they are opposite to each other.
BETA
