MHT CET · Physics · Mechanical Properties of Fluids
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
- A \(\operatorname{mg}\left(1-\frac{\sigma_{1}}{\sigma_{2}}\right)\)
- B \(\operatorname{mg}\left(1-\frac{\sigma_{2}^{\prime}}{\sigma_{1}}\right)\)
- C \(\operatorname{mg}\left(1+\frac{\sigma_{1}}{\sigma_{2}}\right)\)
- D \(\operatorname{mg}\left(1+\frac{\sigma_{2}}{\sigma_{1}}\right)\)
Answer & Solution
Correct Answer
(B) \(\operatorname{mg}\left(1-\frac{\sigma_{2}^{\prime}}{\sigma_{1}}\right)\)
Step-by-step Solution
Detailed explanation
\(\mathrm{F}=\frac{4}{3} \pi \mathrm{r}^{3}\left(\mathrm{~d}_{1}-\mathrm{d}_{2}\right) \mathrm{g}\)
\(\mathrm{F}=\frac{4}{3} \pi \mathrm{r}^{3} \mathrm{~d}_{1}\left(1-\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}\right) \mathrm{g}=\mathrm{M}\left(1-\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}\right) \mathrm{g}\)
\(\mathrm{F}=\frac{4}{3} \pi \mathrm{r}^{3} \mathrm{~d}_{1}\left(1-\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}\right) \mathrm{g}=\mathrm{M}\left(1-\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}\right) \mathrm{g}\)
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