Pressure Due to Liquid Column

Q. Which of the following is the correct gas equation?

1. $\frac{PV}{T}=constant$
2. $\frac{PT}{V}=constant$
3. $\frac{V}{PT}=constant$
4. $\frac{VT}{P}=constant$

Q. From the dimensional consideration, which of the following equation is correct

1. 
2. 
3. 
4. 

Q. Which of the following factors affect pressure in liquid?​

1. Height of liquid column
2. Density of liquid
3. Acceleration due to gravity
4. All of the above

Q.

A plastic mug full of water appears lighter inside water due to

1. Buoyant force

2. Newton's third law

3. Gravitational force

4. Pressure

Q. The pressure exerted by a liquid depends on:

1. area of the liquid surface
2. shape of the liquid surface
3. height of the liquid column
4. volume of the liquid column

Q. Water flows into a large tank with flat bottom at the rate of ${10}^{-4}{m}^3{s}^{-1}.$ Water is also leaking out of a hole of area 1 ${cm}^2$ at its bottom. If the height of the water in the tank remains steady, then this height is :

1. 2.9 cm
2. 5.1 cm
3. 4 cm
4. 1.7 cm

Q.

An equilateral triangle with sides of length $s$ is rotated in space about one side.

Show that the volume of the solid formed is $\frac{1}{4}\pi s^3$ .

Q. Which of the following factors affect pressure in liquid?​

1. Height of liquid column
2. Density of liquid
3. Acceleration due to gravity
4. All of the above

Q.

Write the three factors on which the pressure exerted by a liquid depends.

Q. The size of an air bubble rising up in the water

1. decreases
2. increases
3. may increase or decrease
4. remains the same

Q. Which of the following factors affect pressure in liquid?​

1. Height of liquid column
2. Density of liquid
3. Acceleration due to gravity
4. All of the above

Q. In the top view of a system, area of each piston is different. Which of the following statement is false? Assume the height of the pistons to be the same.

1. Pressure at each piston will be different.
2. Piston having higher area will experience lesser force.
3. Piston having lower area will experience larger force.
4. Pressure at all pistons will be equal.

Q. A tank is filled with water. There is a hole in the bottom. At the bottom total pressure is $3atm(1atm={10}^{5}N/m^2)$, then, the velocity of water flowing from hole is :

1. 10 m/s
2. 20 m/s
3. 15 m/s
4. 25 m/s

Q. A tank full of water has a small hole at the bottom. If one-fourth of the tank is emptied in $t_1$ seconds and the remaining three-fourths of the tank is emptied in $t_2$ seconds. Then the ratio $\frac{t_1}{t_2}$ is

1. $\sqrt{3}$
2. $\sqrt{2}$
3. $\frac{2}{\sqrt{3}}-1$
4. $\frac{1}{\sqrt{2}}$

Q. A large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y$ from the top and the other is a circular hole of radius $R$ at a depth $4y$ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both the holes are the same. Then, $R$ is equal to

1. $L/\sqrt{2\pi }$
2. $2\pi /L$
3. $L$
4. $L/2\pi$

Q. A vessel of area of cross section A has liquid to a height H. There is a hole at the bottom of vessel having area of cross-section a. The time taken to decrease the level from $H_1$ to $H_2$ will be:

1. $\frac{A}{a}\sqrt{\frac{2}{g}}[{\sqrt{H}}_1-{\sqrt{H}}_2]$
2. $\frac{A}{a}\sqrt{\frac{g}{2}}[{\sqrt{H}}_1-{\sqrt{H}}_2]$
3. $\sqrt{2gh}$
4. $\sqrt{2gh(H_1-H_2)}$

Q. $10$ min are taken to empty a rectangular vessel of height $h$ through an orifice in its bottom. How much time will it take to be emptied the vessel when half filled?

1. $5min$
2. $9min$
3. $3min$
4. $7min$

Q. A tank full of water has a small hole at its bottom. If one-fourth of the tank is emptied in $t_1$ seconds and the remaining three fourth of the tank is emptied in $t_2$ seconds, then ratio $\left(t_1/t_2\right)$

1. $\sqrt{3}$
2. $\frac{2-\sqrt{2}}{\sqrt{2}}$
3. $\sqrt{2}$
4. $\frac{2-\sqrt{3}}{\sqrt{3}}$

Q. A cylindrical vessel of height $500mm$ has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice and the water level in the vessel becomes steady with height of water column being $200mm$. Find the fall in height (in mm) of water level due to opening of the orifice. (Take atmospheric pressure $=1.0\times {10}^{5}N/m^2$, density of water $=1000kg/m^3$ and $g=10m/s^2$. Neglect any effect of surface tension.)

Q. A large tank filled with water to a height h is to be emptied through a small hole at the bottom.The ratio of times taken for the level of water to fall from $h$ to $h/2$ and from $h/2$ to $0$ is

1. $\sqrt{2}$
2. $\frac{1}{\sqrt{2}}$
3. $\sqrt{2}-1$
4. $\frac{1}{\sqrt{2}-1}$

Q. The vessels A, B, C and D have the water level as shown in figure. Pressure exerted by water is the maximum in_______.

1. vessel A
2. vessel B
3. vessel D
4. vessel C

Q. A rectangular tank is filled to the brim with water. When a hole at its bottom is unplugged, the tank is emptied in time $T$. If the tank is half-filled with water, it will be emptied in time:

1. $\frac{T}{\sqrt{2}}$
2. $\frac{T}{\sqrt{3}}$
3. $\frac{T}{2}$
4. $\frac{T}{2\sqrt{2}}$

Q. A container is placed on a table has four holes. The ${\text{X}}_{\text{A}},{\text{X}}_{\text{B}},{\text{X}}_{\text{C}}$and ${\text{X}}_{\text{D}}$ represent the horizontal distances covered by the liquid coming out from the holes $\text{A},\text{B},\text{C},$ and $\text{D}$ respectively. Which of the following options is correct?

1. ${\text{X}}_{\text{A}}>{\text{X}}_{\text{B}}>{\text{X}}_{\text{C}}>{\text{X}}_{\text{D}}$
2. ${\text{X}}_{\text{A}}<{\text{X}}_{\text{B}}<{\text{X}}_{\text{C}}<{\text{X}}_{\text{D}}$
3. $({\text{X}}_{\text{A}}={\text{X}}_{\text{B}})>{\text{X}}_{\text{C}}>{\text{X}}_{\text{D}}$
4. $({\text{X}}_{\text{A}}={\text{X}}_{\text{B}})<{\text{X}}_{\text{C}}<{\text{X}}_{\text{D}}$

Q. There is a small hole in the bottom of a fixed container containing a liquid up to height "h". The top of the liquid, as well as the hole at the bottom, are exposed to the atmosphere. As the liquid comes out of the hole: (Area of the hole is "a' and that of the top surface is "A')

1. The top surface of the liquid accelerates with acceleration = $g\frac{a^2}{2A^2}$
2. The top surface of the liquid accelerates with acceleration = g
3. The top surface of the liquid accelerates with acceleration = $g\frac{a}{A}$
4. The top surface of the liquid accelerates with acceleration = $\frac{g{a}^2}{A^2}$

Q. A tank full of water has a small hole at its bottom. If one-fourth of the tank is emptied in $t_1$ seconds and the remaining three fourth of the tank is emptied in $t_2$ seconds, then ratio $\left(t_1/t_2\right)$ is:

1. $\sqrt{3}$
2. $\sqrt{2}$
3. $\frac{2-\sqrt{2}}{\sqrt{2}}$
4. $\frac{2-\sqrt{3}}{\sqrt{3}}$

Q. A cylindrical vessel of height $h$ and base area $S$ is filled with water. An orifice of area $s\ll S$ is opened in the bottom of the vessel. Neglecting the viscosity of water, time taken by all the water to pour out of the vessel.

Q.

Two identical cubes A and B are placed in a tank containing a liquid as shown below. Choose the correct statement regarding pressures exerted on them.

1. The pressure experienced by cube A is more.

2. The pressure experienced by cube B is more.

3. The pressure experienced by cubes A and B are equal.

4. We need to know density of the liquid to compare the pressures experienced by cubes A and B.

Q. $Case1$: A balloon is fitted to the valve at the bottom of a cylinder which is half filled with water.

$Case2$: A balloon is fitted to the valve at the bottom of a cylinder which is fully filled with water.

Both the cylinder and valves are identical. In which case will the balloon bulge more out when the valves are opened?

1. $Case1$

2. $Case2$

3. Both equally

4. Balloon will not bulge

Q. Find out the ratio of $P_1$ and $P_2$. The value of $F_1$ and $F_2$ are $2N$ and $3N$.

1. $\frac{P_1}{P_2}=1:2$
2. $\frac{P_1}{P_2}=1:3$
3. $\frac{P_1}{P_2}=2:3$
4. $\frac{P_1}{P_2}=1:1$

Q. A cylindrical vessel of $90cm$ height is kept filled up to the brim. It has four holes four holes $1$, $2$, $3$ and $4$ which are respectively, at height of $20cm$, $30cm$, $40cm$ and $50cm$ from the horizontal floor $PQ$. The water falling at the horizontal distance from the vessel comes from

1. hole number $4$
2. hole number $2$
3. hole number $3$
4. hole number $1$