A ball of density $\mathrm{\sigma }$ and radius r is dropped on the surface of a liquid of density $\mathrm{\rho }$ from certain height. If speed of ball does not change even on entering in liquid and viscosity of liquid is $\mathrm{\eta }$, then the height from which ball dropped is

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

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

3. $\frac{2(\mathrm{\sigma }-\mathrm{\rho }){\mathrm{gr}}^2}{9\mathrm{\eta }}$

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

Viscous drag force depends on

1. Size of body

2. Velocity with which it moves

3. Viscosity of fluid

4. All of these

The terminal velocity of a small sized spherical body of radius r falling vertically in a viscous liquid is related to radius r as-

1. $\mathrm{v}\propto \frac{1}{{\mathrm{r}}^2}$

2. $\mathrm{v}\propto {\mathrm{r}}^2$

3. $\mathrm{v}\propto \frac{1}{\mathrm{r}}$

4. $\mathrm{v}\propto \mathrm{r}$

A spherical ball is dropped in a long column of viscous liquid. The speed v of the ball varies as function of time as

1. 

2. 

3. 

4. 

On putting a capillary tube in a pot filled with water, the level of water rises upto a height of 4 cm in the tube. If a tube of half the diameter is used instead, the water will rise to a height nerly

1. 2 cm

2. 4 cm

3. 8 cm

4. 11 cm

Soap helps in cleaning clothes, because

1. It attracts the dirt particles

2. It decreases the surface tension of water

3. It increases the cohesive force between water molecules

4. It increases the angle of contact

On increasing temperature of a liquid, its surface tension generally

1. Increases

2. Decreases

3. Remains constant

4. First increases and then decreases

The raincoats are made water proof by coating it with a material, which

1. Absorb water

2. Increase surface tension of water

3. Increase the angle of contact

4. Decreases the density of water

An iron needle slowly placed on the surface of water floats because

1. It displaces water more than its weight

2. The density of material of needle is less than that of water

3. Of surface tension

4. Of its shape

Two water droplets merge with each other to form a larger droplet. In this process

1. Energy is liberated

2. Energy is absorbed

3. Energy is neither liberated nor absorbed

4. Some mass is converted into energy