A solid uniform ball of volume V floats on the interface of two immiscible liquids (Fig.) The specific gravity of the upper liquid is ${\mathrm{\rho }}_1$ and that of lower one is ${\mathrm{\rho }}_2$ whilst the specific gravity of ball is $\mathrm{\rho } ({\mathrm{\rho }}_1<\mathrm{\rho }<{\mathrm{\rho }}_2)$. The fraction of the volume of the ball in the upper liquid is

   

1. $\frac{{\mathrm{\rho }}_2}{{\mathrm{\rho }}_1}$

2. $\frac{{\mathrm{\rho }}_2-\mathrm{\rho }}{{\mathrm{\rho }}_2-{\mathrm{\rho }}_1}$

3. $\frac{\mathrm{\rho }-{\mathrm{\rho }}_1}{{\mathrm{\rho }}_2-{\mathrm{\rho }}_1}$

4. $\frac{{\mathrm{\rho }}_1}{{\mathrm{\rho }}_2}$

 A metal sphere connected by a string is dipped in a liquid of density $\rho$ as shown in figure. The pressure at the bottom of the vessel will be, ($p_0$atmospheric pressure)

1. p=$p_0+\rho gh$

2. $p>p_0+\rho gh$

3. $p<p_0+\rho gh$

4. $p_0$

Two soap bubbles of radii ${\mathrm{r}}_1 \mathrm{and} {\mathrm{r}}_2$ equal to 4 am and 5 sm are touching each other over a common surface ${\mathrm{S}}_1{\mathrm{S}}_2$ (shown in figure). Its radius will be

1. 4 cm

2. 20 cm

3. 5 cm

4. 4.5 cm

A piece of ice is floating in a beaker containing water when ice melts the temperature falls from 20$°$C to 4$°$C, level of water

1. remains uncharged

2. falls

3. rises

4. changes erratically

The work done in blowing a bubble of radius is W, then the work done in making a bubble of radius 2R from that solution is

1. $\frac{W}{2}$

2. 2W

3. 4W

4. $2^{\frac{1}{3}}W$

When the system shown in the adjoining figure is in equilibrium and if the areas of cross section of the smaller piston and bigger piston are a and 10 a mass on smaller and bigger pistons are  m amd M, then

1. m=M

2. m= 10M

3. M= 10 m

4. M= 100 m

A wooden block, with a coin placed on its top, floats in water as shown in fig. the distance l and h are shown there. After some time the coin falls into the water. Then

1. l decreases and h increases

2. l increases and h decreases

3. Both l and h increase

4. Both l and h decrease

What is the velocity v of a metallic ball of radius r failing in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body? (The densities of metal and of liquid are $\rho$ and $\sigma$ respectively, and the viscosity of the liquid is h)

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

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

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

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

5. $\frac{{\mathrm{r}}^2\mathrm{g}}{18\mathrm{\eta }}(\mathrm{\rho }-2\mathrm{\sigma })$

A tank is filled with water upto a height H. Water is allowed to come out of a hole P in one pf the walls at a depth D below the surface of water. Express the horizontal distance x in terms of H and D

1. $\mathrm{x}=\sqrt{\mathrm{D}(\mathrm{H}-\mathrm{D})}$

2. $\mathrm{x}=\sqrt{\frac{\mathrm{D}(\mathrm{H}-\mathrm{D})}{2}}$

3. $\mathrm{x}=2\sqrt{\mathrm{D}(\mathrm{H}-\mathrm{D})}$

4. $\mathrm{x}=4\sqrt{\mathrm{D}(\mathrm{H}-\mathrm{D})}$

A U-tube od uniform cross section as shown in figure is partially filled with a liquid I. Another liquid II which does not mix with liquid I is poured into one side. It is found that the liquid levels of the two sides of the tube are the same, while the level of liquid I has risen by 2cm. If the specific gravity of liquid I is 1.1 the specific gravity of liquid II must be
                        

1. 1.12

2. 1.1

3. 1.05

4. 1.0