Question 325: Properties of Matter

Question

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

Accepted Answer

Power = rate of production of heat = F.V
= 6$$\pi $$$$\eta $$rV
T
.V
T
= = 6$$\pi $$$$\eta $$rV
T
2
[ As F = 6$$\pi $$$$\eta $$rV
T
from stokeÃ¢ÂÂs formula ]
$$ \because $$ Terminal velocity V
T
= $${{2{r^2}\left( {ho  - \sigma } ight)g} \over {9\eta }}$$
$$ 	herefore $$ V
T
$$ \propto $$ r
2
$$ 	herefore $$ Power $$ \propto $$ 6$$\pi $$$$\eta $$r$$\left[ {{{4{r^4}{{\left( {ho  - \sigma } ight)}^2}{g^2}} \over {81{\eta ^2}}}} ight]$$
$$ \Rightarrow $$ Power $$ \propto $$ r
5

Answer

r3

Answer

r2

Answer

r5

Answer

r4

Properties of Matter

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

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