A capillary tube is immersed vertically in the water and the height of the water column is x. When this arrangement is taken into a mine of depth d, the height of the water column is y. If R is the radius of the earth, the ratio x/y is :

1.  $\left(1 - \frac{\mathrm{d}}{\mathrm{R}}\right)$

2.  $\left(1 - \frac{2\mathrm{d}}{\mathrm{R}}\right)$

3.  $\left(\frac{\mathrm{R} - \mathrm{d}}{\mathrm{R} + \mathrm{d}}\right)$

4.  $\left(\frac{\mathrm{R} + \mathrm{d}}{\mathrm{R} - \mathrm{d}}\right)$

When an air bubble of radius r rises from the bottom to the surface of the lake, its radius becomes $\raisebox{1ex}{$5r$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$. Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature) :

1.  11.2 m

2.  8.7 m

3.  9.5 m

4.  10.5 m

A balloon with mass m is descending down with an acceleration a (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration a?

1. $\frac{2\mathrm{ma}}{\mathrm{g} +\hspace{0.17em}\mathrm{a}}$

2. $\frac{2\mathrm{ma}}{\mathrm{g} - \mathrm{a}}$

3. $\frac{\mathrm{ma}}{\mathrm{g} +\hspace{0.17em}\mathrm{a}}$

4. $\frac{\mathrm{ma}}{\mathrm{g} - \mathrm{a}}$

A liquid X of density 3.36 g ${\mathrm{cm}}^{-3}$ is poured in the right arm of a U-tube, which contains Hg. Another liquid Y is poured in the left arm with a height of 8 cm. Upper levels of X and Y are the same. What is the density of Y?

1. 0.8 ${\mathrm{gcc}}^{-1}$

2. 1.2 ${\mathrm{gcc}}^{-1}$

3. 1.4 ${\mathrm{gcc}}^{-1}$

4. 1.6 ${\mathrm{gcc}}^{-1}$

A wooden block, with a coin placed on its top, floats in water as shown in the figure. The distances h and l are shown there. After some time, the coin falls into the water, then :

1. Both l and h increase

2. Both l and h decrease

3. l decreases and h increases

4. l increases and h decreases

The velocity of water in a river is 18 km/hr near the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The coefficient of viscosity of water = ${10}^{-2}$ poise.

1.  ${10}^{-1} \mathrm{N}/{\mathrm{m}}^2$

2.  ${10}^{-2} \mathrm{N}/{\mathrm{m}}^2$

3.  ${10}^{-3} \mathrm{N}/{\mathrm{m}}^2$

4.  ${10}^{-4} \mathrm{N}/{\mathrm{m}}^2$

Water rises in a vertical capillary tube upto a height of 2.0 cm . If the tube is inclined at an angle of $60°$ with the vertical, then upto what length the water will rise in the tube ?

1. 2.0 cm                             

2. 4.0 cm
3. $\frac{4}{\sqrt{3}}\mathrm{cm}$                             

4.$2\sqrt{2}\mathrm{cm}$

Two capillary tubes of 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. $\frac{9}{10}$

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

1. Increase                     

2. Decrease

3. Unchanged                 

4. None of these

If the capillary experiment is performed in a vacuum, then for a liquid the capillary will: