A metal sphere of mass 'm' and density ' $\sigma_{1}$ ' falls with terminal velocity through a container…

A metal sphere of mass 'm' and density ' $\sigma_{1}$ ' falls with terminal velocity through a container containing liquid. The density of liquid is ' $\sigma_{2}$ '. The viscous force acting on the sphere is
  1. $\operatorname{mg}\left(1-\frac{\sigma_{1}}{\sigma_{2}}\right)$
  2. $\operatorname{mg}\left(1-\frac{\sigma_{2}}{\sigma_{1}}\right)$
  3. $\operatorname{mg}\left(1+\frac{\sigma_{1}}{\sigma_{2}}\right)$
  4. $\operatorname{mg}\left(1+\frac{\sigma_{2}}{\sigma_{1}}\right)$

Solution

$\mathrm{F}=\frac{4}{3} \pi \mathrm{r}^{3}\left(\mathrm{~d}_{1}-\sigma_{2}\right) \mathrm{g}$ $\mathrm{F}=\frac{4}{3} \pi \mathrm{r}^{3} \mathrm{~d}_{1}\left(1-\frac{\sigma_{2}}{\mathrm{~d}_{1}}\right) \mathrm{g}=\mathrm{M}\left(1-\frac{\sigma_{2}}{\mathrm{~d}_{1}}\right) \mathrm{g}$

Asked in: MHT CET 2020 (15 Oct Shift 1)

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