On putting a capillary tube in a pot filled with water, the level of water rises upto a height of 4 cm in the tube. If a tube of half the diameter is used instead, the water will rise to a height of nearly

Question

On putting a capillary tube in a pot filled with water, the level of water rises upto a height of 4 cm in the tube. If a tube of half the diameter is used instead, the water will rise to a height of nearly (A) 2 cm (B) 4 cm (C) 8 cm (D) 11 cm

Tardigrade Admin · Accepted Answer

For capillary tube h=(2 T/r ρ g) We can say h propto (1/r) text or h propto (1/d) So, (h1/h2)=(d2/d1) ⇒ (4/x)=(d/2 d) ⇒ x=8 cm

Q. On putting a capillary tube in a pot filled with water, the level of water rises upto a height of $4 c m$ in the tube. If a tube of half the diameter is used instead, the water will rise to a height of nearly

2 cm

4 cm

8 cm

11 cm

For capillary tube
$h = \frac{2 T}{r ρ g}$
We can say
$h \propto \frac{1}{r} or h \propto \frac{1}{d}$
So, $\frac{h _{1}}{h _{2}} = \frac{d _{2}}{d _{1}}$
$\Rightarrow \frac{4}{x} = \frac{d}{2 d}$
$\Rightarrow x = 8 c m$

Q. On putting a capillary tube in a pot filled with water, the level of water rises upto a height of 4cm in the tube. If a tube of half the diameter is used instead, the water will rise to a height of nearly