Mechanical Properties of Fluids - Result Question 14
14. A capillary tube of radius $r$ is immersed in water and water rises in it to a height $h$. The mass of the water in the capillary is $5 g$. Another capillary tube of radius $2 r$ is immersed in water. The mass of water that will rise in this tube is :
[2020]
(a) $5.0 g$
(b) $10.0 g$
(c) $20.0 g$
(d) $2.5 g$
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Answer:
Correct Answer: 14. (b)
Solution:
- (b) Force of surface tension balances the weight of water in capillary tube.
$F_S=2 \pi r T \cos \theta=m g$
Here, $T$ and $\theta$ are constant.
So, $m \propto r$
Let $m_1$ and $m_2$ be the mass of water in two capillary tube.
$\therefore \frac{m_2}{m_1}=\frac{r_2}{r_1}$
$\Rightarrow \frac{m_2}{5.0}=\frac{2 r}{r}$
$(\because r_2=2 r)$
$\Rightarrow m_2=10.0 g$
