Question

A large bottle is fitted with a capillary tube at the bottom. The ratio of times taken to empty the bottle when it is first filled with water and next with oil of relative density $0.8$ is $[{\eta }_{water}={10}^{-3}Pa.s{\eta }_{oil}=2\times {10}^{-3}Pa.s]$

• A. $5:2$
• B. $2:3$
• C. $3:4$
• D. $1:2$

Answer 1

The correct option is A $5:2$

The ratio of time taken to empty the bottle will be proportional to $(Q{)}_{flow}$ rate different types of liquids

$Q_{water}:Q_{oil}$

$\frac{\pi P_1\left(gh\right)r^4}{8\eta L}:\frac{\pi P_2{r}^4\left(gh\right)}{8{\eta }_{2}L}$

$=\frac{1}{{10}^{-3}}:\frac{0.8}{2\times {10}^{-3}}$

$=2:0.8=5:2$