Pressure

Q.

If the value of atmospheric pressure is ${10}^{6}dynec{m}^{-2}$, then its value in SI units is:

1. ${10}^{4}N{m}^{-2}$
2. ${10}^{6}N{m}^{-2}$
3. ${10}^{5}N{m}^{-2}$
4. ${10}^{3}N{m}^{-2}$

Q.

To what temperature must a neon gas sample be heated to double its pressure if the initial volume of gas at $75°\mathrm{C}$ is decreased by $15.0\%$ by cooling the gas?

Q.

A 50 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter 1.0 cm. What is the pressure exerted by the heel on the horizontal floor?

Q. A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides, as shown in the figure. The radius of vessel is $5\text{cm}$ and the angular speed of rotation is $\omega {\text{rad s}}^{–1}$. The difference in the height, $h\text{(in cm)}$ of liquid at the centre of the vessel and at the side will be :

1. $\frac{2{\omega }^2}{25g}$
2. $\frac{5{\omega }^2}{2g}$
3. $\frac{25{\omega }^2}{2g}$
4. $\frac{{\omega }^2}{25g}$

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. With increase in altitude, atmospheric pressure

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

Q. A container has two immiscible liquids of densities ${\rho }_1$ and ${\rho }_2(>{\rho }_1)$. A capillary tube of radius $r$ is inserted in the liquid so that its bottom reaches upto the denser liquid. The denser liquid rises in the capillary and attains a height $h$ from the interface of the liquids, which is equal to the column length of the lighter liquid. Assuming angle of contact to be zero, the surface tension of heavier liquid is

1. $2\pi r{\rho }_2\text{gh}$
2. $\frac{{\rho }_{2}rgh}{2}$
3. $\frac{r}{2}({\rho }_2-{\rho }_1)\text{gh}$
4. $2\pi r({\rho }_2-{\rho }_1)\text{gh}$

Q.

The pressure acting on a submarine is $3\times {10}^{5}Pa$ at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be :(Assume that atmospheric pressure is $1\times {10}^{5}Pa$, the density of water is ${10}^{3}kg{m}^{-3}$, acceleration due to gravity $g=10m{s}^{-2}$)

1. $\left(\frac{200}{3}\right)\%$

2. $\left(\frac{5}{200}\right)\%$

3. $\left(\frac{200}{5}\right)\%$

4. $\left(\frac{3}{200}\right)\%$

Q. The upper edge of a gate in a dam runs along the water surface. The gate is $2\text{m}$ high and $4\text{m}$ wide and is hinged along the horizontal line through its top. Find the torque( in $\text{kN~m}$) due to the force from water about the top edge of the gate.

Q. Two vessels $A$ and $B$ of different shapes have the same base area and are filled with water upto the same height $h$ (as shown). The force exerted by water on the base is $F_A$ for vessel $A$ and $F_B$ for vessel $B$. The respective weights of water in the vessels are $W_A$ and $W_B$. Then

1. $F_A>F_B;W_A>W_B$
2. $F_A=F_B;W_A>W_B$
3. $F_A=F_B;W_A<W_B$
4. $F_A>F_B;W_A=W_B$

Q.

An ideal gas is trapped between a mercury column and the closed-end of a narrow vertical tube of uniform base containing the column. The upper end of the tube is open to the atmosphere. The atmospheric pressure equals 76 cm of mercury. The lengths of the mercury column and the trapped air column are 20 cm and 43 cm respectively. What will be the length of the air column when the tube is tilted slowly in a vertical plane through an angle of ${60}^0$ ? Assume the temperature to remain constant.

Q.

A ball whose density is $0.4\times {10}^{3}mg/m^3$ falls into water from a height of 9cm. To what depth does the ball sink?

1. 6 cm

2. 9 cm

3. 4.5 cm

4. 2.25 cm

Q.

Describe the activity to determine the density of a liquid using density bottle.

Q. At a depth of $500\text{m}$ under an ocean, what is the absolute pressure? Given density of sea water is $1.03\times {10}^3{\text{kg/m}}^3$. (Take $g=10{\text{m/s}}^2$ & $1\text{atm}={10}^5\text{Pa}$)

1. $51.5\text{atm}$
2. $53.5\text{atm}$
3. $50.5\text{atm}$
4. $52.5\text{atm}$

Q.

A uniform tube closed at one end, contains a pellet of mercury 10 cm long. When the tube is kept vertically with the closed-end upward, the length of the air column trapped is 20 cm. Find the length of the air column trapped when the tube is inverted so that the closed-end goes down. Atmospheric pressure = 75 cm of mercury.

Q.

Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density $984kg{m}^{–3}$ . Determine the height of the wine column for normal atmospheric pressure.

Q. Why lowering of vapour pressure is not a collegave property

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

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

Q. A column of mercury of length 10 cm is contained in the middle of a horizontal tube of length 1m which is closed at both the ends. The two equal lengths contain air at standard atmospheric pressure of 0.76 m of mercury. The tube is now turned to vertical position. By what approximate distance (in cm) will the column of mercury be displaced?

Q. In case of a simply supported $I-$section beam of span $L$ and loaded with a central load $W$, the length of elasto-plastic zone of the plastic hinge is

1. $\frac{L}{2}$
2. $\frac{L}{3}$
3. $\frac{L}{4}$
4. $\frac{L}{5}$

Q.

A vessel of volume $V_0$ contains an ideal gas at pressure $p_0$ and temperature T. Gas is continuously pumped out of this vessel at a constant volume -rate dV/dt = r keeping the temperature constant. The pressure of the gas being taken out equals the pressure inside the vessel. Find (a) the pressure of the gas as a function of time, (b) the time taken before half the original gas is pumped out.

Q. Calculate the solid angle subtended by an octant of a sphere at the centre of the sphere.

1. $\frac{\pi }{2}\text{steradian}$
2. $\frac{\pi }{4}\text{steradian}$
3. $\frac{\pi }{6}\text{steradian}$
4. $\pi \text{steradian}$

Q. Figure shows a container filled with a liquid of density $\rho$. Four points $A,B,C\text{and}D$ lie on the diametrically opposite points of a circle as shown. Points $A$ and $C$ lie on a vertical line and points $B$ and $D$ lie on a horizontal line. $P_A,P_B,P_C,P_D$ are the absolute pressures at the respective points. Then, the correct statement(s) is/are :

1. $P_D=P_B$
2. $P_A<P_B=P_D<P_C$
3. $P_D=P_B=\frac{P_C-P_A}{2}$
4. $P_D=P_B=\frac{P_C+P_A}{2}$

Q. A spherical body of radius $R$ consists of a fluid of constant density and is in equilibrium under its own gravity. If $P\left(r\right)$ is the pressure at $r(r<R)$, then the correct option(s) is (are)

1. $P(r=0)=0$
2. $\frac{P(r=3R/4)}{P(r=2R/3)}=\frac{63}{80}$
3. $\frac{P(r=3R/5)}{P(r=2R/5)}=\frac{16}{21}$
4. $\frac{P(r=R/2)}{P(r=R/3)}=\frac{20}{27}$

Q.

During blood transfusion the needle is inserted in a vein where the gauge pressure is 2000 Pa. At what height must the blood container be placed so that blood may just enter the vein? [Use the density of whole blood from Table 10.1].

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. By sucking through a straw, a student can reduce the pressure in his lungs to $750\text{mm}$ of $Hg$ (density $=13.6{\text{gm/cm}}^3$). Using the straw, he can drink water from a glass upto a maximum depth of :

1. $10\text{cm}$
2. $75\text{cm}$
3. $1.36\text{cm}$
4. $13.6\text{cm}$

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

Q.

The approximate depth of an ocean is 2700m. The compressibility of water is $45.4\times {10}^{-11}P{a}^{-1}$ and density of water is ${10}^{3}kg/m^3$. What fractional compression of water will be obtained at the bottom of the ocean?

1. $1.4\times {10}^{-2}$

2. $0.8\times {10}^{-2}$

3. $1\times {10}^{-2}$

4. $1.2\times {10}^{-2}$

Q. Which of the following diagrams correctly shows the relation between the terminal velocity $V_T$ of a spherical body falling in a liquid and viscosity $\nu$ of the liquid?

1. 
2. 
3. 
4.