Mechanical Properties of Fluids - Result Question 12

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12. A small sphere of radius ’ $r$ ’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to

======= ####12. A small sphere of radius ’ $r$ ’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/mechanical-properties-of-fluids/mechanical-properties-of-fluids—result-question-12.md (a) $r^{3}$

(c) $r^{4}$

(b) $r^{2}$

(d) $r^{5}$

[2018]

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Answer:

Correct Answer: 12. (d)

Solution:

  1. (d) Power $=$ rate of production of heat $=F \cdot V$

$=6 \pi \eta r V_T \cdot V_T=6 \pi \eta r V_T^{2}$

$(\because F=6 \pi \eta V_T r.$ stoke’s formula)

$V_T \propto r^{2}$ $\because \quad V_T=\frac{2}{9} \frac{r^{2}(\rho-\sigma)}{\eta} g$

$\therefore \quad$ Power $\propto r^{5}$