Question

59. A very narrow capillary tube records a rise of 20cm when dipped in water. When the area of cross-section is
reduced to one-fourth of the former value, water will rise to a height of:
(a) 10cm
(b) 20cm
fet 40cm
(d) 80cm​

Answer 1

Answer is Option (b)

Explanation:

• Let A be are of cross-section of tube.

then new area after changes made $(A') = \frac {A}{2}$

or $\frac {A}{2}$is directly proportional to  radius.

Also, Height of rise, h = $\frac {2T Cos\theta}{\rho rg}$

or h = $\frac {1}{r}$

Hence, h', change in height = $\sqrt 2h$

$h' = \sqrt 2 \times 20$ or $20\sqrt 2 cm$

Rise in height of Level = 20 cm