Question

In a capillary tube, water rises to a height of 4 cm. If the cross sectional area of the tube were one – fourth, water would have raised to a height of

• A. 2 cm
• B. 4 cm
• C. 8 cm
• D. 16 cm

Answer 1

The correct option is C

8 cm

Cross sectional area of the tube, A =$\pi r^2$

Height of capillary rise is given by, $h=\frac{2\tau }{\rho gr}\Rightarrow h\propto \frac{1}{r}$

But $r\propto \sqrt{A}$ . Hence $h\propto \frac{1}{r}\Rightarrow \frac{h_1}{h_2}=\sqrt{\frac{A_2}{A_1}}=\sqrt{\frac{1}{4}}$

$\therefore h_2=2h_1=8cm$