Two capillary tubes P and Q are dipped vertically in water. The height of water level in capillary tube P is (2 rd /3) of the height in capillary tube Q. The ratio of their diameter is

Question

Two capillary tubes P and Q are dipped vertically in water. The height of water level in capillary tube P is (2 rd /3) of the height in capillary tube Q. The ratio of their diameter is (A) 2: 3 (B) 3: 2 (C) 3: 4 (D) 4: 3

Tardigrade Admin · Accepted Answer

r=(2 T cos θ/ρ g h) As we know r propto (1/h) ( r P / r Q )=( h Q / h P )=( h /(2)3 h ) ⇒ ( r p / r Q )=(3/2)

Q. Two capillary tubes $P$ and $Q$ are dipped vertically in water. The height of water level in capillary tube $P$ is $\frac{2 ^{r d}}{3}$ of the height in capillary tube $Q$ . The ratio of their diameter is

$2 : 3$

$3 : 2$

$3 : 4$

$4 : 3$

$r = \frac{2 T c o s θ}{ρ g h}$
As we know $r \propto \frac{1}{h}$
$\frac{r _{P}}{r _{Q}} = \frac{h _{Q}}{h _{P}} = \frac{h}{\frac{2}{3} h}$
$\Rightarrow \frac{r _{p}}{r _{Q}} = \frac{3}{2}$

Q. Two capillary tubes P and Q are dipped vertically in water. The height of water level in capillary tube P is 32rd​ of the height in capillary tube Q. The ratio of their diameter is

2:3

3:2

3:4

4:3