Two rain drops of same radii 'r', falling with terminal velocity 'v' merge and form a bigger drop of radius R. The terminal velocity of the bigger drop is

1. $v\frac{R}{r}$

2. $v\frac{R^2}{r^2}$

3. v

4. 2v

Water flows along a horizonatl pipe whose cross-section is not constant. The pressure is 1 cm of Hg where the velocity is 35 ${\mathrm{cms}}^{-1}$. At a point where the velocity is $65 {\mathrm{cms}}^{-1}$, the pressure will be

1. 0.89 cm of Hg

2. 8.9 cm of Hg

3. 0.5 cm of Hg

4. 1 cm of Hg

If two soaps bubbles of equal radii r coalesce  then the radius of curvature of interface between two bubble will be

1. r

2. 0

3. infinity

4. $\frac{r}{2}$

A cylinrical vessel is filled with a liquid up to a height H. A small hole is made in the vessel at a distance y below the liquid surface as shown in figure. The  liquid emerging from the hole strike the ground at distance x

1. x is equal if hole is at depth y or H-y

2. x is maximum for y=$\frac{\mathrm{H}}{2}$

3. Both (1.) and (2) are correct

4. Both (1.) and (2.) are wrong

Water from a tap emerges vertically down with an initial speed of 10${\mathrm{ms}}^{-1}$. The cross-sectional area of tap is ${10}^{-4}{\mathrm{m}}^2$. Assume that the pressure is constant throughout the stream of water, and that the flow is steady. The cross sectional area of the stream 0.15 m below the tap is

1. $5.0\times {10}^{-4}{\mathrm{m}}^2$

2. $10\times {10}^{-5} {\mathrm{m}}^2$

3. $5.0\times {10}^{-5} {\mathrm{m}}^2$

4. $2.0\times {10}^{-5} {\mathrm{m}}^2$

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