A shell having a hole of radius r is dipped in water. It holds the water up to a depth of h then the value of r is

(1) $\mathrm{r}=\frac{2\mathrm{T}}{\mathrm{hdg}}$

(2) $\mathrm{r}=\frac{\mathrm{T}}{\mathrm{hdg}}$

(3) $\mathrm{r}=\frac{\mathrm{Tg}}{\mathrm{hd}}$

(4) None of these

In a capillary tube, the water rises by 1.2 mm. The height of water that will rise in another capillary tube having half the radius of the first, is 

(1) 1.2 mm

(2) 2.4 mm

(3) 0.6 mm

(4) 0.4 mm

If the capillary experiment is performed in a vacuum, then for a liquid there capillary rise 

(1) It will rise

(2) Will remain the same

(3) It will fall

(4) Rise to the top

If liquid level falls in a capillary then radius of capillary will

(1) Increase                     

(2) Decrease

(3) Unchanged                 

(4) None of these

Water rises to a height \(\mathrm{h}\) in a capillary at the surface of earth. On the surface of the moon, the height of water column in the same capillary will be:
1. \(\mathrm{6h}\)                           
2. $\frac{1}{6}\mathrm{h}$
3.  \(\mathrm{h}\)                             
4. \(\mathrm{zero}\)

Two capillary tubes of the same diameter are put vertically one each in two liquids whose relative densities are 0.8 and 0.6 and surface tensions are 60 and 50 dyne/cm respectively Ratio of heights of liquids in the two tubes $\frac{{\mathrm{h}}_1}{{\mathrm{h}}_2}$ is

(1) $\frac{10}{9}$

(2) $\frac{3}{10}$

(3) $\frac{10}{3}$

(4) $\frac{9}{10}$

In a capillary tube experiment, a vertical \(30~\text{cm}\) long capillary tube is dipped in water. The water rises up to a height of \(10~\text{cm}\) due to capillary action. If this experiment is conducted in a freely falling elevator, the length of the water column becomes:
1. \(10~\text{cm}\)
2. \(20~\text{cm}\)
3. \(30~\text{cm}\)
4. Zero

Kerosene oil rises up the wick in a lantern

(1) Due to surface tension of the oil

(2) The wick attracts the kerosene oil

(3) Of the diffusion of the oil through the wick

(4) None of the above

Water rises against gravity in a capillary tube when its one end is dipped into water because

(1) Pressure below the meniscus is less than atmospheric pressure

(2) Pressure below the meniscus is more than atmospheric pressure

(3) Capillary attracts water

(4) Of viscosity

There is a horizontal film of soap solution. On it, a thread is placed in the form of a loop. The film is pierced inside the loop and the thread becomes a circular loop of radius \(R.\) If the surface tension of the loop is \(T,\) then what will be the tension in the thread?
1. \(\dfrac{πR^{2}}{T}\)
2. \(πR^{2} T\)
3. \(2 πRT\)
4. \(2 RT\)