WBJEE · Physics · Mechanical Properties of Fluids
Two solid spheres \(S_{1}\) and \(S_{2}\) of same uniform density fall from rest under gravity in a viscous medium and after some time, reach terminal velocities \(v_{1}\) and \(v_{2}\) respectively. If ratio of masses \(\frac{m_{1}}{m_{2}}=8\), then \(\frac{v_{1}}{v_{2}}\) will be equal to
- A 2
- B 4
- C \(\frac{1}{2}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(B) 4
Step-by-step Solution
Detailed explanation
\(\mathrm{v}=\frac{2 \mathrm{r}^{2}}{9 \mathrm{n}}(\mathrm{d}-\rho) \mathrm{y}\) \(\mathrm{m}=\frac{4}{3} \pi \mathrm{r}^{3} \cdot \mathrm{d}\) \(\mathrm{r} \propto \mathrm{m}^{1 / 3}\) \(\Rightarrow \mathrm{v}_{\mathrm{T}} \propto \mathrm{r}^{2} \propto \mathrm{m}^{2 / 3}\)…
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