Pressure

Q.

Where will the atmospheric pressure be greater- at ground level or at top of a high mountain?

Q.

A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half – submerged state. If ${\rho }_c$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

1. More than half - filled if ${\rho }_C$ is less than 0.5

2. More than half - filled ${\rho }_C$ is more than 1.0

3. Half - filled if ${\rho }_c$ is more than 0.5

4. Less than half - filled if ${\rho }_c$ is less than 0.5

Q.

Atmospheric pressure increases as we move from sea level to higher altitude.

1. True
2. False

Q. Gauge pressure

1. May be positive
2. May be negative
3. May be zero
4. All of these

Q. Some liquid is filled in a cylindrical vessel of radius $R$. Let $F_1$ be the force applied by the liquid on the bottom of the cylinder. Now the same liquid is poured into a vessel of uniform square cross-section of side $R$. Let $F_2$ be the force applied by the liquid on the bottom of this new vessel. Then:

1. $F_1=\pi F_2$
2. $F_1=\frac{F_2}{\pi }$
3. $F_1=\sqrt{\pi }{F}_2$
4. $F_1=F_2$

Q. Which of the following is not possible?

1. 
2. 
3. 
4. 

Q. If the gauge pressure at the bottom of a water tank is $2.7\text{kPa}$, then what is the depth of the water in the tank?
[Take $g=10{\text{m/s}}^2$]

1. $0.27\text{cm}$
2. $2.7\text{cm}$
3. $27\text{cm}$
4. $270\text{cm}$

Q. The L-shaped fish tank shown in the figure is filled with water and is open at the top. If $d=5.0\text{m}$, what is the ratio of force exerted by the water on face A and face B? (Take $g=10{\text{m/s}}^2$ and neglect atmospheric pressure)

1. $4:5$
2. $5:4$
3. $3:5$
4. $5:3$

Q. Assuming that the atmosphere has the same density anywhere as at sea level $(\rho =1.3{\text{kg/m}}^3)$ and $g$ to be constant $(g=10{\text{m/s}}^2)$, what should be the approximate height of the atmosphere so that the atmospheric pressure at sea level is $p_0=1.01\times {10}^5{\text{N/m}}^2$ ?

1. $6\text{km}$
2. $8\text{km}$
3. $12\text{km}$
4. $18\text{km}$

Q. Variation of atmospheric pressure with height from the surface of the earth is

1. Linear
2. Parabolic
3. Exponential
4. Hyperbolic

Q. A closed tube is filled with liquid $\rho =800{\text{kg/m}}^3$. It is rotating about an axis shown in figure with an angular velocity $\omega =4\text{rad/sec}$ and length of the tube is $9\text{m}$. Find the pressure difference between the ends of the tube.

1. $2\text{bar}$
2. $1\text{bar}$
3. $1.512\text{bar}$
4. $1.728\text{bar}$

Q.

If mercury is replaced with water in barometer, what would be the height of water column at standard atmospheric pressure, i.e., $76cm$ of mercury? (Specific gravity of mercury $=13.6$)

1. $1033.6m$

2. $1033.6cm$

3. $1033.6mm$

4. $10336cm$

Q. Figure shows two containers $P$ and $Q$ with same base area $A$ and each filled upto same height with the same liquid. Select the correct alternative.

1. $P_x=P_y$
2. $P_x>P_y$
3. $P_y>P_x$
4. Cannot say

Q. At a depth of $1000\text{m}$ in an ocean, what is the gauge pressure, when density of sea water is given as $1.03\times {10}^3{\text{kg/m}}^3$? (Take $g=10{\text{m/s}}^2$)

1. $1.04\times {10}^7\text{Pa}$
2. $1.03\times {10}^7\text{Pa}$
3. $1.02\times {10}^7\text{Pa}$
4. $1\times {10}^7\text{Pa}$

Q. An ideal gas is filled in an insulated cylinder fitted with a movable piston connected with an ideal spring (of force constant $K$) as shown in the figure. Initially, the spring is relaxed and the gas in the piston has volume $V_0$ and temperature $T_0$ . Now the gas in the cylinder is heated slowly so that the piston slides towards right to a distance $x$. Find the final pressure and temperature of the gas. (Given atmospheric pressure = $P_0$ and area of cross-section of the cylinder is $A$).

Q. An open container as shown in figure is filled with water $(\rho ={10}^3{\text{kg/m}}^3)$ upto height $8\text{m}$. If it starts moving with acceleration $9.81{\text{m/s}}^2$, determine the pressure difference between points $A$ and $B$.
[Take $g=9.81{\text{m/s}}^2$]

1. $20\text{kPa}$
2. $15\text{kPa}$
3. $10\text{kPa}$
4. $25\text{kPa}$

Q. 3 similar vessels are filled with equal masses of 3 liquids of densities d1, d2, and d3 (d1 > d2 > d3).

1. Pressure at the bottom is equal in all vessels
2. Pressure at the bottom is maximum in vessel A
3. Pressure at the bottom is maximum in vessel B
4. Pressure at the bottom is maximum in vessel C

Q.

If mercury is replaced with water in barometer, what would be the height of water column at standard atmospheric pressure, i.e., $76cm$ of mercury? (Specific gravity of mercury $=13.6$)

1. $1033.6m$

2. $1033.6cm$

3. $1033.6mm$

4. $10336cm$

Q. In the figure shown below, the liquid taken in the siphon is water. Find the pressure difference ($P_B-P_A$) between the points $A$ and $B$.

1. $400{\text{N/m}}^2$
2. $3000{\text{N/m}}^2$
3. $1000{\text{N/m}}^2$
4. Zero

Q. If the gauge pressure at the bottom of a water tank is $2.7\text{kPa}$, then what is the depth of the water in the tank?
[Take $g=10{\text{m/s}}^2$]

1. $0.27\text{cm}$
2. $2.7\text{cm}$
3. $27\text{cm}$
4. $270\text{cm}$

Q.

A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half – submerged state. If ${\rho }_c$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

1. More than half - filled if ${\rho }_C$ is less than 0.5

2. More than half - filled ${\rho }_C$ is more than 1.0

3. Half - filled if ${\rho }_c$ is more than 0.5

4. Less than half - filled if ${\rho }_c$ is less than 0.5

Q. A 5m tank is half filled with water and half with oil of density 0.85 g/cc. The pressure at the bottom is

1. 1.85 g/sq.cm
2. 89.25 g/sq.cm
3. 462.5 g/sq.cm
4. 500 g/sq.cm

Q. With increase in altitude, atmospheric pressure

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

Q. Select the correct one from the statements given below:
$\left(i\right)$ At any point in a static fluid, pressure acting on it will be same in all directions.
$\left(ii\right)$ Forces acting on a fluid in equilibrium have to be parallel to the surface.

1. $\left(i\right)$ only
2. $\left(ii\right)$ only
3. Both $\left(i\right)\&\left(ii\right)$
4. None of these.

Q. There is a circular tube in a vertical plane. Two liquids are filled in the tube whose densities are given by $373{\text{kg/m}}^3$ and $100{\text{kg/m}}^3$ respectively . It is observed that the liquids do not mix and each liquid subtends an angle of ${90}^{\circ }$ at the centre. Radius joining their interfaces makes an angle $\alpha$ with the vertical as shown in figure. Find the value of $\alpha$ (in degrees) is

Q. Some liquid is filled in a cylindrical vessel of radius $R$. Let $F_1$ be the force applied by the liquid on the bottom of the cylinder. Now the same liquid is poured into a vessel of uniform square cross-section of side $R$. Let $F_2$ be the force applied by the liquid on the bottom of this new vessel. Then:

1. $F_1=\pi F_2$
2. $F_1=\frac{F_2}{\pi }$
3. $F_1=\sqrt{\pi }{F}_2$
4. $F_1=F_2$

Q. The variation of pressure with elevation is $P=P_0{e}^{-\frac{Mgh}{RT}}$ where $h$ is the elevation, $M$ is the molecular weight of air, $R$ is the universal gas constant and $T$ is the temperature. What are the assumptions involved while calculating pressure with the above given expression?

1. Density is constant from zero elevation to the point at higher elevation.
2. Temperature is constant from zero elevation to the point at higher elevation.
3. Air is assumed to follow ideal gas law.
4. None of the above

Q. An ideal gas is filled in a cylinder, which is fitted with a movable non-conducting piston as shown in the figure. The gas in the cylinder is heated slowly. The gas expands and pistons moves towards right. If the temperature of the gas is increased slowly from $T_0$ to $2T_0$, find the displacement of the piston. (Given atmospheric pressure = $P_0$ and area of cross-section of the cylinder = $A$).

1. $\frac{V_0}{2A}$
2. $\frac{5V_0}{2A}$
3. $\frac{2V_0}{3A}$
4. $\frac{V_0}{A}$

Q. A vessel of volume $2{\text{m}}^3$ contains an ideal gas at pressure ${10}^5{\text{N/m}}^2$ and temperature $300\text{K}$. The gas is continously pumped out of this vessel at a constant volume rate $\frac{dV}{dt}=2\times {10}^{-3}{\text{m}}^3/\text{s}$ , keeping the temperature constant. The pressure of the gas being taken out equals the pressure inside the vessel. Find the time taken before half of the original gas is pumped out (in minutes).

1. $5.5\text{min}$
2. $11.55\text{min}$
3. $10.5\text{min}$
4. $21.5\text{min}$

Q. Arrangement of pipes carrying fluids of densities ${\rho }_1,{\rho }_2\&{\rho }_3$ is shown in the figure below. If the pipe carrying fluid of density ${\rho }_1$ makes an angle $\theta$ with the horizontal, then what is the value of ${}^{\prime }{h}^{\prime }$ ?

1. $h=\frac{({\rho }_1+{\rho }_1)}{{\rho }_2}l\sin \theta$
2. $h=\left(\frac{{\rho }_3}{{\rho }_2}\right)l\sin \theta$
3. $h=\left(\frac{{\rho }_3-{\rho }_1}{{\rho }_2}\right)l\sin \theta$
4. $h=\left(\frac{{\rho }_2}{{\rho }_3}\right)\text{tan}\theta$