Two soap bubbles of radii r₁ and r₂ equal to 4 cm and 5 cm are touching each other over a common surface S₁S₂ (shown in figure). Radius of common surface will be

1. 4 cm

2. 20 cm

3. 5 cm

4. 4.5 cm

Two capillaries made of same material but of different radii are dipped in a liquid. The rise of liquid in one capillary is 2.2 cm and that in the other is 6.6 cm. The ratio of their radii is

1. 9 : 1

2. 1 : 9

3. 3 : 1

4. 1 : 3

In a surface tension experiment with a capillary tube water rises upto 0.1 m. If the same experiment is repeated on an artificial satellite, which is revolving around the earth, water will rise in the capillary tube upto a height of

1. 0.1 m

2. 0.2 m

3. 0.98 m

4. Full length of the capillary tube

A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions. If T is the surface tension of soap solution, the energy spent in the blowing is

1. $3{\mathrm{\pi Tr}}^2$

2. $6{\mathrm{\pi Tr}}^2$

3. $12{\mathrm{\pi Tr}}^2$

4. $24{\mathrm{\pi Tr}}^2$

At which of the following temperatures, the values of surface tension of water is minimum

1. $4°\mathrm{C}$

2. $25°\mathrm{C}$

3. $50°\mathrm{C}$

4. $75°\mathrm{C}$

The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be 75 cm of Hg and the density of water to be 1/10 of the density of mercure, the depth of the lake is

1. 5 m

2. 10 m

3. 15 m

4. 20 m

A hemispherical bowl just floats without sinking in a liquid of density $1.2\times {10}^3<mspace\; width="1em"></mspace>\mathrm{kg}/{\mathrm{m}}^3$. If outer diameter and the density of the bowl are 1 m and $2\times {10}^4<mspace\; width="1em"></mspace>\mathrm{kg}/{\mathrm{m}}^3$ respecitvely, then the inner diameter of the bowl will be

1. 1.94 m

2. 1.97 m

3. 0.98 m

4. 1.99 m

Spherical ball of radius 'r' is falling in a viscous fluid of viscosity '$\mathrm{\eta }$' with a velocity 'v'. The retarding viscous force acting on the spherical ball is

1. Inversely proportional to 'r' but directly proportional to velocity 'v'

2. Directly proportional to both radius 'r' and velocity 'v'

3. Inversely proportional to both radius 'r' and velocity 'v'

4. Directly proportional to 'r' but inversely proportional to 'v'

A ball of radius r and density $\mathrm{\rho }$ falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is $\mathrm{\eta }$, the value of h is given by

1. $\frac{2}{9}{\mathrm{r}}^2\left(\frac{1-\mathrm{\rho }}{\mathrm{\eta }}\right)\mathrm{g}$

2. $\frac{2}{81}{\mathrm{r}}^2\left(\frac{\mathrm{\rho }-1}{\mathrm{\eta }}\right)\mathrm{g}$

3. $\frac{2}{81}{\mathrm{r}}^4{\left(\frac{\mathrm{\rho }-1}{\mathrm{\eta }}\right)}^2\mathrm{g}$

4. $\frac{2}{9}{\mathrm{r}}^4{\left(\frac{\mathrm{\rho }-1}{\mathrm{\eta }}\right)}^2\mathrm{g}$

A sniper fires a rifle bullet into a gasoline tank making a hole 53.0 m below the surface of gasoline. The tank was sealed at 3.10 atm. The stored gasoline has a density of 660 kgm^-3. The velocity with which gasoline begins to shoot out of the hole is

1. 27.8 ms^-1

2. 41.0 ms^-1

3. 9.6 ms^-1

4. 19.7 ms^-1