A container has a small hole at its bottom. Area of cross-section of the hole is $A_1$ and that of the container is $A_2$. Liquid is poured in the containor at a constant rate Q $m^3/s$
The maximum level of liquid in the container will be

(1) $\frac{Q^2}{2g A_1{A}_2}$

(2) $\frac{Q^2}{2g {A_1}^2}$

(3) $\frac{Q}{2g A_1{A}_2}$

(4) $\frac{Q^2}{2g {A_2}^2}$

A rectangular vessel when full of water takes 10 minutes to be emptied through an orifice in its bottom. How much time will it take to be emptied when half filled with water

1. 9 minute

2. 7 minute

3. 5 minute

4. 3 minute

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