Chapter 12

Density of ice is \(\rho\) and that of water is \(\sigma\). What will be the decrease in volume when a mass \(M\) of ice melts? (a) \(\frac{M}{\sigma-\rho}\) (b) \(\frac{a-\rho}{M}\) (c) \(M\left(\frac{1}{\rho}-\frac{1}{\sigma}\right)\) (d) \(\frac{1}{M}\left(\frac{1}{\rho}-\frac{1}{\sigma}\right)\)

A \(50 \mathrm{~kg}\) girl wearing high heel shoes balances on a single heel. If the heel is circular with a diameter \(1.0 \mathrm{~cm}\). What is the pressure exerted on the horizontal floor? (a) \(6.9 \times 10^{6} \mathrm{~Pa}\) (b) \(6.2 \times 10^{6} \mathrm{~Pa}\) (c) \(9.6 \times 10^{6} \mathrm{~Pa}\) (d) \(9.0 \times 10^{6} \mathrm{~Pa}\)

The surface area of air bubble increases four times when it rises from bottom to top of a water tank where the temperature is uniform. If the atmospheric pressure is \(10 \mathrm{~m}\) of water, the depth of the water in the tank is (a) \(30 \mathrm{~m}\) (b) \(40 \mathrm{~m}\) (c) \(70 \mathrm{~m}\) (d) \(80 \overline{\mathrm{m}}\)

A U-tube contains water and methylated spirit separated by mereury. The mercury columns in the two arms are in level with \(10.0 \mathrm{~cm}\) of water in one arm and \(12.5 \mathrm{~cm}\) of spirit in the other. The specific gravity of spirit would be. (a) \(0.70\) (b) \(0.80\) (c) \(0.90\) (d) \(0.60\)

A cylindrical vessel is filled with equal amounts of weight of mercury on water. The overall height of the two layers is \(29.2 \mathrm{~cm}\), specific gravity of mercury is 13.6. Then the pressure of the liquid at the bottom of the vessel is (a) \(29.2 \mathrm{~cm}\) of water (b) 29.2/13.6 cm of mercury (c) \(4 \mathrm{~cm}\) of mercury (d) \(15.6 \mathrm{~cm}\) of mercury

A uniform rod of density \(\rho\) is placed in a wide tank containing a liquid o \((\sigma>\rho)\). The depth of liquid in the tank is half the length of the rod. The rod is in equilibrium, with its lower end resting on the bottom of the tank. In this position, the rod makes an angle \(\theta\) with the horizontal. Then, \(\sin \theta\) is equal to (a) \(\frac{1}{2} \sqrt{\frac{\sigma}{\rho}}\) (b) \(\frac{1}{2} \frac{\sigma}{\rho}\) (c) \(\sqrt{\frac{\rho}{a}}\) (d) \(\sqrt{\frac{\rho}{d}}\)

The U-tube has a uniform cross-section as shown in figure. A liquid is filled in the two arms upto heights \(h_{1}\) and \(h_{2}\) and then the liquid is allowed to move. Neglect viscosity and surface tension. When the level equalize in the two arms, the liquid will (a) be at rest (b) be moving with an acceleration of \(g\left(\frac{h_{1}-h_{2}}{h_{1}+h_{2}+2}\right)\) (c) be moving with a velocity of \(\left(h_{1}-h_{2}\right) \sqrt{\frac{g}{2\left(h_{1}+h+h\right)}}\) (d) exert a net force to the right on the cube

A beaker containing water is balanced on the pan of a common balance. A solid of specific gravity 1 and mass \(5 \mathrm{~g}\) is tied to the arm of the balance and immersed in water contained in the beaker. The scale pan with the beaker (a) goes down (b) goes up (c) remains unchanged (d) None of these

Torricelli's barometer used mercury. Paseal duplicated it using French wine of density \(984 \mathrm{~kg} / \mathrm{m}^{2} .\) Determine the height of the wine column for normal atmospheric pressure. (a) \(9.5 \mathrm{~cm}\) (b) \(5.5 \mathrm{~cm}\) (c) \(10.5 \mathrm{~cm}\) (d) \(11.5 \mathrm{~cm}\)

An ice block floats in a liquid whose density is less than water. A part of bloek is outside the liquid. When whole of ice has melted, the liquid level will (a) rise (b) go down (c) remain same (d) first rise then go down

A block is submerged in vessel filled with water by a spring attached to the bottom of the vessel. In equilibrium, the spring is compressed. The vessel now moves downwards with an acceleration \(a(

A balloon of volume \(1500 \mathrm{~m}^{3}\) and weighing \(1650 \mathrm{~kg}\) with all its equipment is filled with He (density \(0.2 \mathrm{~kg} \mathrm{~m}^{-3}\) ). If the density of air be \(1.3 \mathrm{kgm}^{-3}\), the pull on the rope tied to the balloon will be (a) \(300 \mathrm{~kg}\) (b) \(1950 \mathrm{~kg}\) (c) \(1650 \mathrm{~kg}\) (d) zero

A cubie block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with acceleration of \(g / 3\) the fraction of volume immersed in the liquid will be (a) \(\frac{1}{2}\) (b) \(\frac{3}{8}\) (c) \(\frac{2}{3}\) (d) \(\frac{3}{4}\)

A wooden ball of density \(\rho\) is immersed in water of density \(\rho_{0}\) to depth \(h\) and then released. The height \(H\) above the surface of water upto which the ball jump out of water is (a) zero (b) \(h\) (c) \(\frac{\rho_{0} h}{\rho}\) (d) \(\left(\frac{\rho_{0}}{\rho}-1\right) h\)

Two cubes each weighing \(22 \mathrm{~g}\) exactly are taken. One is of iron \(\left(d=8 \times 10^{3} \mathrm{kgm}^{-1}\right)\) and the other is of marble \(\left(D=3 \times 10^{3} \mathrm{kgm}^{-3}\right)\). They are immersed in alcohol and then weighed again (a) iron cube weighs less (b) iron cube weighs more (c) both have equal weight (d) nothing can be said

The spring balance \(A\) reads \(2 \mathrm{~kg}\) with a block of mass \(m\) suspended from it. A balance \(B\) reads \(5 \mathrm{~kg}\) when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in a beaker as shown in figure. (a) The balance A will read more than \(2 \mathrm{~kg}\) (b) The balance \(B\) will read less than \(5 \mathrm{~kg}\) (c) The balance \(A\) will read less than \(2 \mathrm{~kg}\) and \(B\) will read more than \(5 \mathrm{~kg}\) (d) The balance \(A\) will read more than \(2 \mathrm{~kg}\) and \(B\) will read less than \(5 \mathrm{~kg}\)

A cylinder of mass \(m\) and density \(\rho\) hanging from a string is lowered into a vessel of cross-sectional area \(A\) containing a liquid of density \(\sigma(<\rho)\) until it is fully immersed. The increase in pressure at the bottom of the vessel is (a) Zcro (b) \(\frac{m g}{A}\) (c) \(\frac{m g \rho}{a A}\) (d) \(\frac{\operatorname{mog}}{\rho \mathrm{A}}\)

A piece of gold weights \(50 \mathrm{~g}\) in air and \(45 \mathrm{~g}\) in water. If there is a cavity inside the piece of gold, then find its volume [Density of gold \(=19.3 \mathrm{~g} / \mathrm{cc}]\). (a) \(2.4 \mathrm{~cm}^{3}\) (b) \(2.4 \mathrm{~m}^{3}\) (c) \(4.2 \mathrm{~m}^{3}\) (d) \(4.2 \mathrm{~mm}^{7}\)

An alloy of \(\mathrm{Zn}\) and Cu (i.e., brass) weights \(16.8 \mathrm{~g}\) in air and \(14.7 \mathrm{~g}\) in water. If relative density of \(\mathrm{Cu}\) and \(\mathrm{Zn}\) are \(8.9\) and \(7.1\) respectively then determine the amount of \(\mathrm{Zn}\) and \(\mathrm{Cu}\) in the alloy. (a) \(2 \mathrm{~g} .4 \mathrm{~g}\) (b) \(4 \mathrm{~g}, 2 \mathrm{~g}\) (c) 9.345g. \(7.455 \mathrm{~g}\) (d) \(0,3 \mathrm{~g}\)

A rectangular plate \(2 \mathrm{~m} \times 3 \mathrm{~m}\) is immersed in water in such a way that its greatest and least depth are \(6 \mathrm{~m}\) and \(4 \mathrm{~m}\) respectively, from the water surface. The total thrust on the plate is (a) \(294 \times 10^{3} \mathrm{~N}\) (b) \(294 \mathrm{~N}\) (c) \(100 \times 10^{7} \mathrm{~N}\) (d) \(400 \times 10^{1} \mathrm{~N}\)

Two soap bubbles \(A\) and \(B\) are kept in closed chamber where the air is maintained at pressure \(8 \mathrm{~N} / \mathrm{m}^{2}\). The radius of bubbles \(A\) and \(B\) are \(2 \mathrm{em}\) and \(4 \mathrm{~cm}\) respectively surface tension of the soap water used to make bubbles is \(0.04 \mathrm{~N} / \mathrm{m}\). Find the ratio \(n_{B} / n_{A}\), where \(n_{A}\) and \(n_{B}\) are the number of moles of air in bubbles \(A\) and \(B\) respectively [Neglect the effect of gravity] (a) 2 (b) 9 (c) 8 (d) \(\overline{6}\)

A body of density \(\rho\) is dropped from rest at a height \(h\) into a lake of density \(\sigma\), where \(\sigma>\rho\). Neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface. (a) \(\frac{h}{a-\rho}\) (b) \(\frac{h \rho}{\sigma}\) (c) \(\frac{h \rho}{\sigma-\rho}\) (d) \(\frac{h \sigma}{\sigma-\rho}\)

A glass tube \(80 \mathrm{~cm}\) long and open at both ends is half immersed in mercury. Then the top of the tube is closed and it is taken out of the mercury. A column of mercury \(20 \mathrm{~cm}\) long then remains in the tube. The atmospheric pressure (in \(\mathrm{cm}\) of \(\mathrm{Hg}\) ) is (a) 90 (b) 75 (c) 60 (d) 45

Two cylinders of same cross-section and length \(L\) but made of two material of densities \(\rho_{1}\) and \(\rho_{2}\) (in CGS units) are cemented together to form a cylinder of length \(2 L\). If the combination floats in water with a length \(L / 2\) above the surface of water and \(\rho_{1}<\rho_{2}\), then (a) \(\rho_{1}>1\) (b) \(p_{1}<3 / 4\) (c) \(\rho_{1}>1 / 2\) (d) \(\rho_{1}>3 / 4\)

The density of ice is \(0.9 \mathrm{gcc}^{-1}\) and that of sea water is \(1.1 \mathrm{gec}^{-1}\). An ice berg of volume \(V\) is floating in sea water. The fraction of ice berg above water level is (a) \(1 / 11\) (b) \(2 / 11\) (c) \(3 / 11\) (d) \(4 / 11\)

A solid of density \(D\) is floating in a liquid of density \(d\). If \(v\) is the volume of solid submerged in the liquid and \(V\) is the total volume of the solid, then \(v / V\) is equal to (a) \(\frac{d}{P}\) (b) \(\frac{D}{d}\) (c) \(\frac{D}{(D+d)}\) (d) \(\frac{D+d}{D}\)

Two soap bubbles \(A\) and \(B\) are formed at the two open ends of a tube. The bubble \(A\) is smaller than bubble \(B\). Valve and air can flow freely between the bubbles, then (a] there is no change in the size of the bubbles (b) the two bubbles will become of equal size (c) \(A\) will become smaller and \(B\) will become larget (d) \(B\) will become smaller and \(A\) will become larger

The total weight of a piece of wood is \(6 \mathrm{~kg}\). In the floating state in water its \(\frac{1}{3}\) part remains inside the water. On this floating solid, what maximum weight is to be put such that the whole of the piece of wood is to be drowned in the water? (a) \(12 \mathrm{~kg}\) (b) \(10 \mathrm{~kg}\) (c) \(14 \mathrm{~kg}\) (d) \(15 \mathrm{~kg}\)

Two pieces of glass plate one upon the other with a little water in between them cannot be separated easily because of (a) inctia (b) pressure (c) surface tension (d) viscosity

A hemispherical bowl just floats without sinking in a liquid of density \(1.2 \times 10^{3} \mathrm{kgm}^{-3}\). If outer diameter and the density of the bowl are \(1 \mathrm{~m}\) and \(2 \times 10^{4} \mathrm{kgm}^{-3}\) respectively, then the inner diameter of the bowl will be (a) \(0.94 \mathrm{~m}\) (b) \(0.96 \mathrm{~m}\) (c) \(0.98 \mathrm{~m}\) (d) \(0.99 \mathrm{~m}\)

An aeroplane of \(\operatorname{mass} 3 \times 10^{4} \mathrm{~kg}\) and total wing area of \(120 \mathrm{~m}^{2}\) is in a level flight at some height. The difference in pressure between the upper and lower surfaces of its wings in kilo pascal is \(\left(g=10 \mathrm{~ms}^{-2}\right.\) ) (a) \(2.5\) (b) \(5.0\) (c) \(10.0\) (d) \(12.5\)

A thin metal disc of radius \(r\) float on water surface and bends the surface downwards along the perimeter making an angle \(\theta\) with vertical edge of the disc. If the disc displaces a weight of water \(w\) and surface tension of water is \(T\), then the weight of metal dise is (a) \(2 \pi \tau+w\) (b) \(2 \pi r T \cos \theta-w\) (c) \(2 \pi T \cos \theta+w\) (d) \(w-2 \pi T \cos \theta\)

A vessel whose bottom has round holes with diameter of \(1 \mathrm{~mm}\) is filled with water. Assuming that surface tension acts only at holes, then the maximum height to which the water can be filled in vessel without leakage is (Surface tension of water is \(75 \times 10^{-3} \mathrm{Nm}^{-1}\) and \(g=10 \mathrm{~ms}^{-2}\) ) (a) \(3 \mathrm{~cm}\) (b) \(0.3 \mathrm{~cm}\) (c) \(3 \mathrm{~mm}\) (d) \(3 \mathrm{~m}\)

A ring is cut from a platinum tube \(8.5 \mathrm{~cm}\) internal diameter and \(8.7 \mathrm{em}\) external diameter. It is supported horizontally from a pan of a balance so, that it comes in contact with the water is in glass vessel. If an extra \(3.47 \mathrm{~g}-w t\) is required to pull it away from water, surface tension of water is (a) \(72.07\) dyne \(\mathrm{cm}^{-1}\) (b) \(70.80\) dyne \(\mathrm{cm}^{-1}\) (c) \(65.35\) dyne \(\mathrm{cm}^{-1}\) (d) \(60.00\) dyne \(\mathrm{cm}^{-1}\)

Glycerine flows steadily through a horizontal tube of length \(1.5 \mathrm{~m}\) and radius \(1.0 \mathrm{~cm}\). If the amount of glycerine flowing per second at one end is \(40 \times 10^{-1} \mathrm{~kg} / \mathrm{s}\). What is the pressure difference between the two ends of the tube? (Density of glycerine \(=13 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\) and viscosity of glycerine \(=083 \mathrm{~Pa}-\mathrm{s})\). (a) \(9.75 \times 10^{2} \mathrm{~Pa}\) (b) \(6.75 \times 10^{2} \mathrm{~Pa}\) (c) \(5.75 \times 10^{2} \mathrm{~Pa}\) (d) \(6.95 \times 10^{3} \mathrm{kPa}\)

What is the pressure inside the drop of mercury of radius \(3.00 \mathrm{~mm}\) at room temperature? Surface tension of mercury at that temperature \(\left(20^{\circ} \mathrm{C}\right)\) is \(4.65 \times 10^{-1} \mathrm{~N} / \mathrm{m}\). The atmospheric pressure is \(101 \times 10^{5} \mathrm{~Pa}\). Also give the excess pressure inside the drop. (a) \(1.01 \times 10^{3} \mathrm{~Pa}, 320 \mathrm{~Pa}\) (b) \(1.01 \times 10^{3} \mathrm{~Pa}, 310 \mathrm{~Pa}\) (c) \(310 \mathrm{~Pa}, 1.01 \times 10^{8} \mathrm{~Pa}\) (d) \(320 \mathrm{~Pa}, 1.01 \times 10^{5} \mathrm{~Pa}\)

What is the excess pressure inside a bubble of soap solution of radius \(5.00 \mathrm{~mm}\), given that the surface tension of soap solution at the temperature \(\left(20^{\circ} \mathrm{C}\right)\) is \(2.50 \times 10^{-2} \mathrm{~N} / \mathrm{m}\) ? If an air bubble of the same dimension were formed at a depth of \(40.0 \mathrm{~cm}\) inside a container containing the soap solution (of relative density \(1.20\) ), what would be the pressure inside the bubble? ( 1 atmospheric pressure is \(101 \times 10^{5} \mathrm{~Pa}\) ) (a) \(7,06 \times 10^{5} \mathrm{~Pa}\) (b) \(2.06 \times 10^{5} \mathrm{~Pa}\) (c) \(1.06 \times 10^{5} \mathrm{~Pa}\) (d) \(1.86 \times 10^{5} \mathrm{~Pa}\)

A frame made of a metallic wire enclosing a surface area \(A\) is covered with a soap film. If the area of the frame of metallic wire is reduced by \(50 \%\), the energy of the soap film will be changed by (a) \(100 \%\) (b) \(75 \%\) (c) \(50 \%\) (d) \(25 \%\)

The work done in increasing the size of a rectangular soap film with dimensions \(8 \mathrm{~cm} \times 3.75 \mathrm{~cm}\) to \(10 \mathrm{~cm} \times 6 \mathrm{~cm}\) is \(2 \times 10^{-4} \mathrm{~J}\). The surface tension of the film in \(\mathrm{Nm}^{-1}\) is (a) \(1.65 \times 10^{-2}\) (b) \(3.3 \times 10^{-2}\) (c) \(6.6 \times 10^{-2}\) (d) \(8.25 \times 10^{-2}\)

A mercury drop of radius \(1 \mathrm{~cm}\) is broken into 106 droplets of equal size. The work done is \(\left(S=35 \times 10^{-1} \mathrm{Nm}^{-1}\right)\) (a) \(\left.4.35 \times 10^{-2}\right]\) (b) \(\left.4.35 \times 10^{-3}\right\rfloor\) (c) \(4.35 \times 10^{-6} \mathrm{~J}\) (d) \(4.35 \times 10^{-8} \mathrm{~J}\)

A film of water is found between two straight parallel wires of length \(10 \mathrm{~cm}\) each separated by \(0.2 \mathrm{~cm}\). If their separation is increased by \(1 \mathrm{~mm}\), while still maintaining their parallelism, how much work will have to be done? (surface tension of water is \(\left.7.2 \times 10^{-2} \mathrm{Nm}^{-1}\right)\) (a) \(\left.7.22 \times 10^{-6}\right]\) (b) \(1.44 \times 10^{-5} \mathrm{~J}\) (c) \(\left.2.88 \times 10^{-8}\right]\) (d) \(5.76 \times 10^{-5} \mathrm{~J}\)

A drop of water breaks into two droplets of equal size. In this process, which of the following statements is correct? (a) The sum of the temperatures of the two droplets together is equal to temperature of the original drop (b) The sum of the masses of the two droplets is equal to mass of drop (c) The sum of the radii of the two droplets is equal to the radius of the drop (d) The sum of the surface areas of the two droplets is equal to the surface area of the original drop

Work done in splotting a drop of water of \(1 \mathrm{~mm}\) radius into \(10^{6}\) droplets is (surface tension of water \(\left.72 \times 10^{-3} \mathrm{~J} / \mathrm{m}^{2}\right)\) (a) \(\left.9.8 \times 10^{-5}\right\rfloor\) (b) \(895 \times 10^{-5} \mathrm{~J}\) (c) \(5.89 \times 10^{-5} \mathrm{~J}\) (d) \(5.98 \times 10^{-6} \mathrm{~J}\)

A body of uniform cross-sectional area floats in a liquid of density thrice its value. The portion of exposed height will be (a) \(2 \sqrt{3}\) (b) \(5 / 6\) (c) \(1 / 6\) (d) \(9 / 10\)

A drop of liquid of diameter \(2.8 \mathrm{~mm}\) breaks up into 125 identical drops. The change in energy is nearly \(\left(S=75\right.\) dyne \(\left.\mathrm{cm}^{-1}\right)\) (a) zero (b) \(19 \mathrm{erg}\) (c) 46 erg (d) \(74 \mathrm{erg}\)

Streamline flow is more likely for liquids with |NCERT Exemplar ] (a) high density (b) high viscosity (c) low density (d) low viscosity

A water film is made between two straight parallel wires of length \(10 \mathrm{~cm}\) separated by \(5 \mathrm{~mm}\) from each other. If the distance between the wires is increased by \(2 \mathrm{~mm}\). How much work will be done? Surface tension for water is 72 dyne \(\mathrm{cm}^{-1}\). (a) \(288 \mathrm{erg}\) (b) \(72 \mathrm{erg}\) (c) \(144 \mathrm{crg}\) (d) \(216 \mathrm{crg}\)

What change in surface energy will be noticed when a drop of radius \(R\) splits up inte 1000 droplets of radius \(\boldsymbol{r}\), surface tension \(\boldsymbol{T}\) ? (a) \(4 \pi R^{2} T\) (b) \(7 \pi R^{2} T\) (c) \(16 \pi R^{2} T\) (d) \(36 \pi R^{2} T\)

What is the ratio of surface energy of 1 small drop and 1 large drop if 1000 drops combined to form 1 large drop? (a) \(100: 1\) (b) \(1000: 1\) (c) \(10: 1\) (d) \(1: 100\)

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 \(O_{\pm}\) The height at which the resultant force would have to act to the same torque is (a) \(\frac{h}{6}\) (b) \(\frac{h}{3}\) (c) \(\frac{h}{2}\) (d) \(\frac{2 h}{3}\)