Q130 / 155 · WBJEE 2021 · Physics

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
  • Correct answer
    B
    4
  • C
    $\frac{1}{2}$
  • D
    $\frac{1}{4}$

Solution

$\mathrm{v}=\frac{2 \mathrm{r}^{2}}{9 \mathrm{n}}(\mathrm{d}-\rho) \mathrm{y}$ $\mathrm{m}=\frac{4}{3} \pi \mathrm{r}^{3} \cdot \mathrm{d}$ $\mathrm{r} \propto \mathrm{m}^{1 / 3}$ $\Rightarrow \mathrm{v}_{\mathrm{T}} \propto \mathrm{r}^{2} \propto \mathrm{m}^{2 / 3}$ $\therefore \frac{\mathrm{v}_{1}}{\mathrm{v}_{2}}=\left[\frac{\mathrm{m}_{1}}{\mathrm{~m}_{2}}\right]^{2 / 3}=(8)^{2 / 3}=4$

Hence, the correct answer is option: 'B'.

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