Chapter 12

The angle of contact at the interface of water-glass is \(0^{\circ}\) Ethylalcohol-glass is \(0^{\circ}\), Mercury-glass is \(140^{\circ}\) and Methyliodide-glass is \(30^{\circ} .\) A glass capillary is put in a trough containing one of these four liquids. It is observed that the meniscus is convex. The liquid in the trough is (NCFRT Exemplar] (a) water (b) ethylalcohol (c) mercury (d) methyliodide

Water of density \(\rho\) at a depth \(h\) behind the vertical face of dam whose cross-sectional length is \(\lambda\) and cross-sectional area \(A\). It exerts a horizontal resultant force on the dam tending to slide it along its foundation and a torque tending to overturn the dam about the point \(O_{\pm}\) Pressure on the vertical face of the dam is (a) \(\rho g h\) (b) \(\frac{1}{2} \rho g h\) (c) \(\rho g h^{2}\) (d) \(\frac{1}{2} \rho g h^{2}\)

A plane is in level flight at a constant apeed and each wing has an area of \(25 \mathrm{~m}^{2}\). During flight the speed of the air is \(216 \mathrm{kmh}^{-1}\) over the lower wing surface and \(252 \mathrm{kmh}^{-1}\) over the upper wing surface of each wing of aeroplane. Take density of air \(=1 \mathrm{kgm}^{-3}\) and \(g=10 \mathrm{~ms}^{-2}\) The mass of the plane is (a) \(25 \mathrm{~kg}\) (b) \(250 \mathrm{~kg}\) (c) \(1750 \mathrm{~kg}\) (d) \(3250 \mathrm{~kg}\)

In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are \(70 \mathrm{~m} / \mathrm{s}\) and \(63 \mathrm{~m} / \mathrm{s}\) respectively. What is the lift on the wing, if its area is \(2.5 \mathrm{~m}^{2} ?\) Take the density of air to be \(1.3 \mathrm{~kg} / \mathrm{m}^{3}\). (a) \(5.1 \times 10^{2} \mathrm{~N}\) (b) \(6.1 \times 10^{2} \mathrm{~N}\) \(\left.\begin{array}{ll}(2] & 6\end{array}\right] 0^{3} \mathrm{~N}\)

A plane is in level flight at a constant apeed and each wing has an area of \(25 \mathrm{~m}^{2}\). During flight the speed of the air is \(216 \mathrm{kmh}^{-1}\) over the lower wing surface and \(252 \mathrm{kmh}^{-1}\) over the upper wing surface of each wing of aeroplane. Take density of air \(=1 \mathrm{kgm}^{-3}\) and \(g=10 \mathrm{~ms}^{-2}\) If a plane is in level flight with a speed of \(360 \mathrm{kmh}^{-1}\) then the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surfinee is (a) \(13 \%\) (b) \(9 \%\) (c) \(6.5 \%\) (d) \(4.5 \%\)

A plane is in level flight at a constant apeed and each wing has an area of \(25 \mathrm{~m}^{2}\). During flight the speed of the air is \(216 \mathrm{kmh}^{-1}\) over the lower wing surface and \(252 \mathrm{kmh}^{-1}\) over the upper wing surface of each wing of aeroplane. Take density of air \(=1 \mathrm{kgm}^{-3}\) and \(g=10 \mathrm{~ms}^{-2}\) Pressure difference on each wing of aeroplane is (a) \(5 \mathrm{Nm}^{-2}\) (b) \(50 \mathrm{Nm}^{-2}\) (c) \(350 \mathrm{Nm}^{-2}\) (d) \(650 \mathrm{Nm}^{-2}\)

A plane is in level flight at a constant apeed and each wing has an area of \(25 \mathrm{~m}^{2}\). During flight the speed of the air is \(216 \mathrm{kmh}^{-1}\) over the lower wing surface and \(252 \mathrm{kmh}^{-1}\) over the upper wing surface of each wing of aeroplane. Take density of air \(=1 \mathrm{kgm}^{-3}\) and \(g=10 \mathrm{~ms}^{-2}\) Percentage of velocity difference of the upper and lower surface of the wings of aeroplane is (a) \(14.39\) (b) \(15.4 \%\) (c) \(16.7 \%\) (d) \(17.49\)

Water rises to a height of \(16.3 \mathrm{~cm}\) in a capillary of height \(18 \mathrm{~cm}\) above the water level. If the tube is cut at a height of \(12 \mathrm{~cm}\) in the capillary tube, (a) water will come as a fountain from the capillary tube (b) water will stay at a height of \(12 \mathrm{~cm}\) in the capillary tube (c) the height of water in the capillary tube will be \(10.3 \mathrm{~cm}\) (d) water height flow down the sides of the capllary tube

A plane is in level flight at a constant apeed and each wing has an area of \(25 \mathrm{~m}^{2}\). During flight the speed of the air is \(216 \mathrm{kmh}^{-1}\) over the lower wing surface and \(252 \mathrm{kmh}^{-1}\) over the upper wing surface of each wing of aeroplane. Take density of air \(=1 \mathrm{kgm}^{-3}\) and \(g=10 \mathrm{~ms}^{-2}\) The total upward force on the plane is (a) \(250 \mathrm{~N}\) (b) \(2500 \mathrm{~N}\) (c) \(17500 \mathrm{~N}\) (d) \(32500 \mathrm{~N}\)

Assertion-Reason type. Each of these contains two Statements: Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes \((a)\), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion When height of a tube is less than calculated height of liquid in the tube, the liquid does not overflow. Reason The meniscus of liquid at the top of the tube becomes flat.

Assertion-Reason type. Each of these contains two Statements: Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes \((a)\), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion The velocity of flow of a liquid is smaller where pressure is larger and vice-kersa. Reason This is in accordance with Bernoulli's theorem.

By inserting a capillary tube upto a depth \(l\) in water, the water rises to a height \(h\). If the lower end of the capillary tube is closed inside water and the capillary is taken out and closed end opened, to what height the water will remain in the tube, when \(l>h\) ? (a) zero (b) \(l+h\) (c) \(2 h\) (d) \(h\)

Assertion-Reason type. Each of these contains two Statements: Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes \((a)\), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion A hydrogen filled balloon stops rising after it has attained a certain height in the sky. Reason The atmospheric pressure decreases with height and becomes zero when maximum height is attained.

Two capillary tubes of radii \(0.2 \mathrm{~cm}\) and \(0.4 \mathrm{~cm}\) are dipped in the same liquid. The ratio of heights through which liquid will rise in the tubes is (a) \(1: 2\) (b) \(2: 1\) (c) \(1: 4\) (d) \(4: 1\)

Assertion-Reason type. Each of these contains two Statements: Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes \((a)\), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion For the flow to be streamline, value of critical velocity should be as low as possible. Reason Once the actual velocity of flow of a liquid becomes greater than the critical velocity, the flow becomes turbulent.

Water rises in a capillary tube to a height \(h .\) Choose the false statement regarding rise from the following. (a) On the surface of Jupitor, height will be less than \(h\). (b) In a lift, maving up with constant acccleration, height is less than \(h\). [c\\} On the surface of the moon, the height is more than \(h\). (d) In a lift moving down with constant acceleration, height is less than \(h\).

Assertion-Reason type. Each of these contains two Statements: Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes \((a)\), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion A bubble comes from the bottom of a lake to the top. Reason Its radius increases.

The surface tension of a liquid at its boiling point (a) becomes zero (b) becomes infinity (c) is equal to the value at room temperature (d) is half to the value at the room temperature

A body floats in a liquid contained in a beaker. If the whole system falls under gravity, then the upthrust on the body due to liquid is IUP SEE 2009] (a) equal to the weight of the body in air (b) equal to the weight of the body in liquid (c) zero (d) equal to the weight of the immersed part of the body

When a pinch of salt or any other salt which is soluble in water is added to water, its surface tension (a) increases (b) decreases (c) may increase or decrease depending upon salt (d) None of the above

A cube made of material having a density of \(0.9 \times 10^{3} \mathrm{kgm}^{-3}\) floats between water and a liquid of density \(0.7 \times 10^{3} \mathrm{kgm}^{-3}\), which is immiscible with water. What part of the cube is immersed in water? [BVP Fngg, 2008] (a) \(\frac{1}{3}\) (b) \(\frac{2}{3}\) (c) \(\frac{3}{4}\) (d) \(\frac{3}{7}\)

At which of the following temperatures, the value of surface tension of water is minimum? (a) \(4^{\circ} \mathrm{C}\) (b) \(25^{\circ} \mathrm{C}\) (c) \(50^{\circ} \mathrm{C}\) (d) \(75^{\circ} \mathrm{C}\)

A body floats with one-third of its volume consider water and \(3 / 4\) of its volume outside another liquid. The density of other liquid is (a) \(\frac{9}{4} \mathrm{~g} / \mathrm{cc}\) (b) \(\frac{4}{9} \mathrm{~g} / \mathrm{cc}\) (c) \(\frac{8}{3} \mathrm{~g} / \mathrm{cc}\) (d) \(\frac{3}{8} \mathrm{~g} / \mathrm{cc}\)

Bernoulli's theorem is a consequence of the law of conservation of TUP SEE 2008] (a) momentum (b) mass (c) cnergy (d) angular momentum

The aurface tension of soap solution is \(0.03 \mathrm{Nm}^{-1}\). The work done in blowing to form a soap bubble of surface area \(40 \mathrm{~cm}^{2}\), in joule is (a) \(1.2 \times 10^{-4}\) (b) \(2.4 \times 10^{-4}\) (c) \(12 \times 10^{-4}\) (d) \(24 \times 10^{-4}\)

A capillary tube of radius \(R\) and length \(L\) is connected in series with another tube of radius \(R / 2\) and length \(L / 4\). If the pressure difference across the two tubes taken together is \(p\), then the ratio of pressure difference across the first tube to that across the second tube is (a) \(1: 4\) (b) \(1: 1\) (c) \(4: 1\) (d) \(2: 1\)

A body weigh \(50 \mathrm{~g}\) in air and \(40 \mathrm{~g}\) in water. How much would it weight in a liquid of specific gravity \(1.5 ?\) |Karmataka CET 2008] [al \(65 \mathrm{~g}\) (b) \(45 \mathrm{~g}\) (c) \(30 \mathrm{~g}\) (d) \(35 \mathrm{~g}\)

The relative velocity of two parallellayers of water is \(8 \mathrm{cms}^{-1}\). If the perpendicular distance between the layers is \(0.1 \mathrm{em}\), then velocity gradient will be (a) \(40 \mathrm{~s}^{-1}\) (b) \(50 \mathrm{~s}^{-1}\) (c) \(60 \mathrm{~s}^{-1}\) (d) \(80 \mathrm{~s}^{-1}\)

Two water pipes \(P\) and \(Q\) having diameter \(2 \times 10^{-2} \mathrm{~m}\) and \(4 \times 10^{-2} \mathrm{~m}\) respectively are joined in series with the main supply line of water. The velocity of water flowing in pipe \(P\) is (a) 4 times that of \(Q\) (b) 2 times that of \(Q\) (c) \(1 / 2\) times that of 0 (d) \(1 / 4\) times that of 0

The area of cross-section of one limb of an U-tube is twice that of the other. Both the limbs contains mercury at the same level. Water is poured in the wider tube so that mercury level in it goes down by \(1 \mathrm{~cm}\). The height of water column is (Density of water \(=10^{3} \mathrm{kgm}^{-\text {I }}\), density of mercury \(=13.6 \times 10^{3} \mathrm{kgm}^{-3}\) ) \(\quad\) ?erala CET 200s] (a) \(13.6 \mathrm{~cm}\) (b) \(40.8 \mathrm{~cm}\) (c) \(6.8 \mathrm{~cm}\) (d) \(54.4 \mathrm{~cm}\)

The rate of flow of liquid through a capillary tube of radius \(r\) is \(V\), when the pressure difference across the two ends of the capillary is \(p\). If pressure is increased by \(3 p\) and radius is reduced to \(r / 2\), then the rate of flow becomes (a) \(\sqrt{V / 9}\) (b) \(3 V / 8\) (c) \(V / 4\) (d) \(V / 3\)

A spherical solid ball of volume \(V\) is made of a material of density \(\rho_{1}\). It is falling through a liquid of denaity \(\rho_{2}\left(\rho_{2}>\rho_{1}\right)\). Assume that the liquid applied a viscous force on the ball that is proportional to the square of its speeds \(v\), ie., \(F_{\text {vasous }}=-k v^{2}(k>0)\). The terminal speed of the ball is (a) \(\frac{V g\left(\rho_{1}-p_{2}\right)}{k}\) (b) \(\sqrt{\frac{V_{g\left(\rho_{1}-\beta_{2}\right)}}{k}}\) (c) \(\frac{V g \rho_{1}}{k}\) (d) \(\sqrt{\frac{V g \rho_{1}}{k}}\)

Under a pressure head, the rate of orderly volume flow of liquid through a capillary tube is \(Q\). If the length of capillary tube were doubled and the diameter of the bore is halved, the rate of flow would become (a) \(\frac{Q}{4}\) (b) \(16 Q\) (c) \(\frac{Q}{8}\) (d) \(\frac{0}{32}\)

A soap bubble is charged to a potential of \(16 \mathrm{~V}\). Its radius is, then doubled. The potential of the bubble now \begin{tabular}{l|l} will be & [BVP Engs- 2007] \end{tabular} [a) \(16 \mathrm{~V}\) (b) \(8 \mathrm{~V}\) (c) \(4 \mathrm{~V}\) (d) \(2 \mathrm{~V}\)

The rate of steady volume flow of water through a capillary tube of length \(l\) and radius \(r\) under a pressure difference of \(p\), is \(V\). This tube is connected with another tube of the same length but \(\underline{\text { half the }}\) radius in series. Then the rate of steady volume flow through them is (The pressure difference across the combination is \(p\) ) (a) \(\frac{v}{16}\) (b) \(\frac{v}{17}\) (c) \(\frac{16 \mathrm{~V}}{17}\) (d) \(\frac{17 \mathrm{~V}}{16}\)

The cylindrical tube of a spray pump has a cross-section of \(8 \mathrm{~cm}^{2}\), one end of which has 40 fine holes each of area \(10^{-5} \mathrm{~m}^{2}\). If the liquid flows inside the tube with a speed of \(0.15 \mathrm{~m} \mathrm{~min}^{-1}\), the speed with which the liquid is ejected through the holes is [Karnataka CET 2007] (a) \(50 \mathrm{~ms}^{-1}\) (b) \(5 \mathrm{~ms}^{-1}\) (c) \(0.05 \mathrm{~ms}^{-1}\) (d) \(0.5 \mathrm{~ms}^{-1}\)

A boat at anchor is rocked by waves whose crests are \(100 \mathrm{~m}\) apart and velocity is \(25 \mathrm{~ms}^{-1}\), The boat bounces up once in every [UP SEE 2006\(]\) (a) \(2500 \mathrm{~s}\) (b) \(75 \mathrm{~s}\) (c) \(4 \mathrm{~s}\) (d) \(0.25 \mathrm{~s}\)

A tank is filled with water of density \(1 \mathrm{~g}\) per \(\mathrm{cm}^{\mathrm{3}}\) and oil of density \(0.9 \mathrm{~g} \mathrm{~cm}^{-3}\). The height of water layer is \(100 \mathrm{~cm}\) and of the oil layer is \(400 \mathrm{~cm}\). If \(g=980 \mathrm{cms}^{-2}\), then the velocity of efflux from an opening in the bottom of the tank is (a) \(\sqrt{900 \times 980} \mathrm{cms}^{-1}\) (b) \(\sqrt{1000 \times 980} \mathrm{cms}^{-1}\) (c) \(\sqrt{92 \times 980} \mathrm{cms}^{-1}\) (d) \(\sqrt{920 \times 980} \mathrm{cms}^{-1}\)

A body of density \(D_{1}\) and mass \(M\) is moving downward in glycerine of density \(D_{2}\). What is the viscous force acting on it? [Orisa JEE 2006] (a) \(M g\left(1-\frac{D_{2}}{D_{1}}\right)\) (b) \(M g\left(1-\frac{D_{1}}{D_{2}}\right)\) (c) \(M g D_{1}\) (d) \(M g D_{1}\)

A metallic sphere of mass \(M\) falls through glycerine with a terminal velcity \(v\). If we drop a ball of mass \(8 M\) of same metal into a column of glycerine, the terminal velocity of the ball will be (a) \(2 \underline{\underline{v}}\) (b) \(4 \underline{\mathrm{v}}\) (c) \(8 v\) (d) \(16 \mathrm{v}\)

A body of mass \(120 \mathrm{~kg}\) and density \(600 \mathrm{kgm}^{-3}\) floats in water. What additional mass could be added to the body so that the body will just sink? (a) \(20 \mathrm{~kg}\) (b) \(\mathrm{BO} \mathrm{kg}\) (c) \(100 \mathrm{~kg}\) (d) \(120 \mathrm{~kg}\)

A rain drop of radius \(1.5 \mathrm{~mm}\), experiences a drag force \(F=\left(2 \times 10^{-5} \mathrm{v}\right) \mathrm{N}\), while falling through air from a height \(2 \mathrm{~km}\), with a velocity \(\bar{v} .\) The terminal velocity of the rain drop will be nearly (use \(g=10 \mathrm{~ms}^{-2}\) ) (a) \(200 \mathrm{~ms}^{-1}\) (b) \(80 \mathrm{~ms}^{-1}\) (c) \(7 \mathrm{~ms}^{-1}\) (d) \(3 \mathrm{~ms}^{-1}\)

An incompressible fluid flows steadily through a cylindrical pipe which has radius \(2 R\) at a point \(A\) and radius \(R\) at a point \(B\). Further along the flow of direction if the velocity at point \(A\) is \(v\), its velocity at point \(B\) will be (a) \(v / 4\) (b) \(2 v\) (c) \(4 \underline{v}\) (d) \(-\frac{v}{2}\)

If we dip capillary tubes of different radii \(r\) in water and the water rises to different height \(h\) in them, then we shall have constant (a) \(h / \underline{r^{2}}\) (b) \(h / r\) (c) \(h r^{2}\) (d) \(h r\)

A small iron sphere is dropped from a great height. It attains its terminal velocity after having fallen \(32 \mathrm{~m}\). Then, it covers the rest of the path with terminal velocity only. The work done by air friction during the first \(32 \mathrm{~m}\) of fall is \(W_{1}\). The work done by air friction during the subsequent \(32 \mathrm{~m}\) fall is \(W_{2}\). Then \((a) W_{1}>W_{2}\) (b) \(W_{1}

A bubble rises from bottom of a lake \(90 \mathrm{~m}\) deep. On reaching the surface, its volume becomes (take atmospheric pressure correspond upto \(10 \mathrm{~m}\) of water) [BVP Engg, 2006] (a) 18 times (b) 4 times (c) 8 times (d) 10 times

Water is flowing through a pipe of constant cross-section. At some point the pipe becomes narrow and the cross-section is halved. The speed of water is \mathrm{\\{} I U P ~ S E E ~ 2 0 0 5 ] ~ (a) reduced to zero (b) decreased by factor of 2 (c) increased by a factor of 2 (d) unchanged

The force of cohesion is (a) maximum in solids (b) maximum in liquids (c) maximum in gases (d) same in solid, liquid and \(g a s\)

Water flowing out of the mouth of a tap and falling vertically in streamline flow forms a tapering column, Le., the area of cross-section of the liquid column decreases as it moves down. Which of the following is the most accurate explanation for this? (a) Falling water tries to reach a terminal velocity and hence, reduces the area of cross-section to balance upwand and downward forces (b) As the water moves down, its speed increases and hence, its pressure decreases. It is then compressed by atmosphere (c) The surface tension causes the exposed surface area of the liquid to decrease continuously (d) The mass of water flowing out per second through any cross-section must remain constant. As the water is almost incompressible, so the volume of water flowing out per second must remain constant. As this is equal to velocity \(x\) area, the area decreases as velocity increases

A thin liquid flm formed between a \(\mathrm{U}\) shaped wire and a light slider supports a weight of \(1.5 \times 10^{-2} \mathrm{~N}\). The length of the slider is \(30 \mathrm{~cm}\) and its weight negligible.The surface tension of the liquid film is (a) \(0.0125 \mathrm{Nm}^{-1}\) (b) \(0.1 \mathrm{Nm}^{-1}\) (c) \(0.05 \mathrm{Nm}^{-1}\) (d) \(0.025 \mathrm{Nm}^{-1}\)