MHT CET · Physics · Mechanical Properties of Fluids
A small metal sphere of mass 'M' and density 'd \(_{1}\) ', when dropped in a jar filled with liquid moves with terminal velocity after some time. The viscous force acting on the sphere is \(\left(d_{2}=\right.\) density of liquid, \(\mathrm{g}=\) gravitational acceleration \()\)
- A \(\operatorname{Mg}\left(1-\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}\right)\)
- B \(\mathrm{M}_{g}\left(\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}\right)\)
- C \(\mathrm{M}_{g}\left(1-\frac{\mathrm{d}_{1}}{\mathrm{~d}_{2}}\right)\)
- D \(\mathrm{M} g_{-}\left(\frac{\mathrm{d}_{1}}{\mathrm{~d}_{2}}\right)\)
Answer & Solution
Correct Answer
(A) \(\operatorname{Mg}\left(1-\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}\right)\)
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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