MHT CET · Physics · Mechanical Properties of Fluids
If the terminal speed of a sphere A [density \(\rho_A=7.5 \mathrm{~kg} \mathrm{~m}^{-3}\) ] is \(0.4 \mathrm{~ms}^{-1}\), in a viscous liquid [density \(\rho_{\mathrm{L}}=1.5 \mathrm{~kg} \mathrm{~m}^{-3}\) ], the terminal speed of sphere \(B\) [density \(\rho_B=3 \mathrm{~kg} \mathrm{~m}^{-3}\) ] of the same size in the same liquid is
- A \(0.3 \mathrm{~ms}^{-1}\)
- B \(0.1 \mathrm{~ms}^{-1}\)
- C \(0.2 \mathrm{~ms}^{-1}\)
- D \(0.04 \mathrm{~ms}^{-1}\)
Answer & Solution
Correct Answer
(B) \(0.1 \mathrm{~ms}^{-1}\)
Step-by-step Solution
Detailed explanation
Terminal speed is given by
\(
\begin{aligned}
& \mathrm{V}=\frac{2}{9} \frac{\mathrm{r}^2\left(\rho-\rho_{\mathrm{L}}\right)}{\eta} \\
& \therefore \frac{\mathrm{V}_{\mathrm{A}}}{\mathrm{V}_{\mathrm{B}}}=\frac{\rho_{\mathrm{A}}-\rho_{\mathrm{L}}}{\rho_{\mathrm{B}}-\rho_{\mathrm{L}}}=\frac{7.5-1.5}{3-1.5}=\frac{6}{1.5}=4 \\
& \therefore \mathrm{V}_{\mathrm{B}}=\frac{\mathrm{V}_{\mathrm{A}}}{4}=\frac{0.4}{4}=0.1 \mathrm{~ms}^{-1}
\end{aligned}
\)
\(
\begin{aligned}
& \mathrm{V}=\frac{2}{9} \frac{\mathrm{r}^2\left(\rho-\rho_{\mathrm{L}}\right)}{\eta} \\
& \therefore \frac{\mathrm{V}_{\mathrm{A}}}{\mathrm{V}_{\mathrm{B}}}=\frac{\rho_{\mathrm{A}}-\rho_{\mathrm{L}}}{\rho_{\mathrm{B}}-\rho_{\mathrm{L}}}=\frac{7.5-1.5}{3-1.5}=\frac{6}{1.5}=4 \\
& \therefore \mathrm{V}_{\mathrm{B}}=\frac{\mathrm{V}_{\mathrm{A}}}{4}=\frac{0.4}{4}=0.1 \mathrm{~ms}^{-1}
\end{aligned}
\)
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