Water rises to a height of 2.2 text{ cm} in a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The height $h$ to which a liquid rises in a capillary tube is given by the formula $h = \frac{2T \cos 	heta}{r ho g}$, where $r$ is the radius

Vedclass · Accepted Answer

$4.4$

Vedclass · Answer

(B) The height $h$ to which a liquid rises in a capillary tube is given by the formula $h = \frac{2T \cos 	heta}{r ho g}$, where $r$ is the radius of the tube. Since $h \propto \frac{1}{r}$, and the area of cross-section $A = \pi r^2$, we have $r = \sqrt{\frac{A}{\pi}}$, which implies $r \propto \sqrt{A}$. Therefore, $h \propto \frac{1}{\sqrt{A}}$, or $h_1 \sqrt{A_1} = h_2 \sqrt{A_2}$. Given $h_1 = 2.2 	ext{ cm}$ and $A_2 = \frac{1}{4} A_1$, we have $\sqrt{A_2} = \frac{1}{2} \sqrt{A_1}$. Substituting these values: $2.2 	imes \sqrt{A_1} = h_2 	imes \frac{1}{2} \sqrt{A_1}$. Solving for $h_2$: $h_2 = 2.2 	imes 2 = 4.4 	ext{ cm}$.

Water rises to a height of $2.2 \text{ cm}$ in a glass capillary tube. The height to which the same water rises in another capillary having $\frac{1}{4}$ of the cross-sectional area is: (in $\text{ cm}$)

Similar Questions

If $M$ is the mass of water that rises in a capillary tube of radius $r,$ then the mass of water which will rise in a capillary tube of radius $2r$ is

$A$ $20 \ cm$ long capillary tube is dipped in water. The water rises up to $8 \ cm$. If the entire arrangement is put in a freely falling elevator,the length of the water column in the capillary will be ....... $cm$.

Water rises up to a height $h$ in a capillary tube on the surface of the Earth in a stationary condition. The value of $h$ increases if this tube is taken:

The surface tension for pure water in a capillary tube experiment is

Water rises in a capillary tube kept vertically on the surface of the Earth to a height $h$. Choose the false statement regarding capillary rise from the following $:-$

Vedclass Test Series

Exam Paper Generator

Online Exam Module