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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
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container containing liquid. The density of liquid is ' $\sigma_{2}$ '. The viscous force acting
on the sphere is
Solution:
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Verified Answer
The correct answer is:
$\operatorname{mg}\left(1-\frac{\sigma_{2}^{\prime}}{\sigma_{1}}\right)$
$\mathrm{F}=\frac{4}{3} \pi \mathrm{r}^{3}\left(\mathrm{~d}_{1}-\mathrm{d}_{2}\right) \mathrm{g}$
$\mathrm{F}=\frac{4}{3} \pi \mathrm{r}^{3} \mathrm{~d}_{1}\left(1-\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}\right) \mathrm{g}=\mathrm{M}\left(1-\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}\right) \mathrm{g}$
$\mathrm{F}=\frac{4}{3} \pi \mathrm{r}^{3} \mathrm{~d}_{1}\left(1-\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}\right) \mathrm{g}=\mathrm{M}\left(1-\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}\right) \mathrm{g}$
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