The velocity of a small ball of mass m and density $\mathrm{\rho }$ when dropped in a container filled with glycerine of density $\sigma$ becomes constant after sometime. The viscous force acting on the ball in the final stage is:-

1. $\mathrm{mg}\left(\frac{\mathrm{\sigma }}{\mathrm{\rho }}\right)$

2. $\mathrm{mg}\left(1+\frac{\mathrm{\sigma }}{\mathrm{\rho }}\right)$

3. $\mathrm{mg}\left(1-\frac{\mathrm{\sigma }}{\mathrm{\rho }}\right)$

4. mg

A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :

1. 5.0 g

2. 10.0 g

3. 20.0 g

4. 2.5 g

A liquid does not wet the solid surface if the angle of contact is:

1.  equal to $45°$

2.  equal to $60°$

3.  greater then $90°$

4.  zero 

A barometer is constructed using a liquid ( density = $760 \mathrm{kg}/{\mathrm{m}}^3$ ). What would be the height of the liquid column, when a mercury barometer reads 76 cm? 

$(\mathrm{density} \mathrm{of} \mathrm{mercury} = 13600 \mathrm{kg}/{\mathrm{m}}^3)$

1.  1.36 m 

2.  13.6 m 

3.  136 m 

4.  0.76 m 

A small hole of an area of cross-section 2 $m{m}^2$ is present near the bottom of a fully filled open tank of height 2 m. Taking g= 10 $m/s^2$, the rate of flow of water through the open hole would be nearly:

1. $6.4\times {10}^{-6} m^3/s$

2. $12.6\times {10}^{-6} m^3/s$

3. $8.9\times {10}^{-6} m^3/s$

4. $2.23\times {10}^{-6} m^3/s$

A soap bubble, having a radius of 1 mm, is blown from a detergent solution having a surface tension of $2.5\times {10}^{-2}N/m$. The pressure inside the bubble equals at a point $Z_0$ below the free surface of the water in a container. Taking g= 10 m/$s^2$, density of water = ${10}^{3}kg/m^3$, the value of $Z_0$ is:

1. 0.5 cm

2. 100 cm

3. 10 cm

4. 1 cm

Two small spherical metal balls, having equal masses, are made from materials of densities ${\rho }_1 and {\rho }_2$ such that ${\rho }_1=8{\rho }_2$ and having radii of 1 mm and 2 mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals $\eta$ and whose density is 0.1${\rho }_2$. The ratio of their terminal velocities would be:

1. $\frac{79}{72}$

2. $\frac{19}{36}$

3. $\frac{39}{72}$

4. $\frac{79}{36}$

In a U-tube, as shown in the figure, the water and oil are in the left side and right side of the tube respectively. The height for water and oil columns are 15 cm and 20 cm respectively. The density of the oil is: $[take {\rho }_{water}=1000 kg/m^3]$

1. 1200 $kg/m^3$

2. 750 $kg/m^3$

3. 1000 $kg/m^3$

4. 1333 $kg/m^3$