Chapter 7

Two small drops mercury, each of radius \(\mathrm{r}\), coalesces the form a single large drop. The ratio of the total surface energies before and after the change is. (A) \(1: 2^{(1 / 2)}\) (B) \(2^{(1 / 3)}: 1\) (C) 2: 1 (D) \(1: 2\)

The work done in blowing a soap bubble of \(10 \mathrm{~cm}\) radius is [surface tension of soap solution is \(\\{(3 / 100) \mathrm{N} / \mathrm{m}\\}\) ] (A) \(75.36 \times 10^{-4}\) Joule (B) \(37.68 \times 10^{-4}\) Joule (C) \(150.72 \times 10^{-4}\) Joule (D) \(75.36\) Joule

The work done increasing the size of a soap film from \(10 \mathrm{~cm} \times 6 \mathrm{~cm}\) to \(10 \mathrm{~cm} \times 11 \mathrm{~cm}\) is \(3 \times 10^{-4}\) Joule. The surface tension of the film is (A) \(1.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}\) (B) \(3.0 \times 10^{-2} \mathrm{~N} / \mathrm{m}\) (C) \(6.0 \times 10^{-2} \mathrm{~N} / \mathrm{m}\) (D) \(11.0 \times 10^{-2} \mathrm{~N} / \mathrm{m}\)

A big drop of radius \(R\) is formed by 1000 small droplets of coater then the radius of small drop is (A) \((\mathrm{R} / 2)\) (B) \((\mathrm{R} / 5)\) (C) \((\mathrm{R} / 6)\) (D) \((\mathrm{R} / 10)\)

8000 identical water drops are combined to form a bigdrop. Then the ratio of the final surface energy to the initial surface energy of all the drops together is (A) \(1: 10\) (B) \(1: 15\) (C) \(1: 20\) (D) \(1: 25\)

The relation between surface tension T. Surface area \(\mathrm{A}\) and surface energy \(\mathrm{E}\) is given by. (A) \(\mathrm{T}=(\mathrm{E} / \mathrm{A})\) (B) \(\mathrm{T}=\mathrm{EA}\) (C) \(\mathrm{E}=(\mathrm{T} / \mathrm{A})\) (D) \(\mathrm{T}=(\mathrm{A} / \mathrm{E})\)

A liquid wets a solid completely. The meniscus of the liquid in a sufficiently long tube is (A) Flat (B) Concave (C) Convex (D) Cylindrical

When two soap bubbles of radius \(\mathrm{r}_{1}\) and \(\mathrm{r}_{2}\left(\mathrm{r}_{2}>\mathrm{r}_{1}\right)\) coalesce, the radius of curvature of common surface is........... (A) \(r_{2}-r_{1}\) (B) \(\left[\left(r_{2}-r_{1}\right) /\left(r_{1} r_{2}\right)\right]\) (C) \(\left[\left(\mathrm{r}_{1} \mathrm{r}_{2}\right) /\left(\mathrm{r}_{2}-\mathrm{r}_{1}\right)\right]\) (D) \(\mathrm{r}_{2}+\mathrm{r}_{1}\)

The excess of pressure inside a soap bubble than that of the outer pressure is (A) \((2 \mathrm{~T} / \mathrm{r})\) (B) \((4 \mathrm{~T} / \mathrm{r})\) (C) \((\mathrm{T} / 2 \mathrm{r})\) (D) \((\mathrm{T} / \mathrm{r})\)

The radii of two soap bubbles are \(\mathrm{r}_{1}\) and \(\mathrm{r}_{2} .\) In isothermal conditions two meet together is vacuum Then the radius of the resultant bubble is given by (A) \(\mathrm{R}=\left[\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right) / 2\right]\) (B) \(\mathrm{R}=\mathrm{r}_{1}\left(\mathrm{r}_{1}+\mathrm{r}_{2}+\mathrm{r}_{3}\right)\) (C) \(\mathrm{R}^{2}=\mathrm{r}_{1}^{2}+\mathrm{r}_{2}^{2}\) (D) \(\mathrm{R}=\mathrm{r}_{1}+\mathrm{r}_{2}\)

A spherical drop of coater has radius \(1 \mathrm{~mm}\) if surface tension of contex is \(70 \times 10^{-3} \mathrm{~N} / \mathrm{m}\) difference of pressures between inside and outside of the spherical drop is (A) \(35 \mathrm{~N} / \mathrm{m}^{2}\) (B) \(70 \mathrm{~N} / \mathrm{m}^{2}\) (C) \(140 \mathrm{~N} / \mathrm{m}^{2}\) (D) zero

In capillary pressure below the curved surface at water will be (A) Equal to atmospheric (B) Equal to upper side pressure (C) More than upper side pressure (D) Lesser than upper side pressure

If the excess pressure inside a soap bubble is balanced by oil column of height \(2 \mathrm{~mm}\) then the surface tension of soap solution will be. \((\mathrm{r}=1 \mathrm{~cm}\) and density \(\mathrm{d}=0.8 \mathrm{gm} / \mathrm{cc})\) (A) \(3.9 \mathrm{~N} / \mathrm{m}\) (B) \(3.9 \times 10^{-2} \mathrm{~N} / \mathrm{m}\) (C) \(3.9 \times 10^{-3} \mathrm{~N} / \mathrm{m}\) (D) \(3.9 \times 10^{-1} \mathrm{~N} / \mathrm{m}\)

A capillary tube of radius \(\mathrm{R}\) is immersed in water and water rises in it to a height \(\mathrm{H}\). Mass of water in the capillary tube is M. If the radius of the tube is doubled. Mass of water that will rise in the capillary tube will now be (A) \(\mathrm{M}\) (B) \(2 \mathrm{M}\) (C) \((\mathrm{M} / 2)\) (D) \(4 \mathrm{M}\)

A vesel whose bottom has round holes with diameter of \(0.1 \mathrm{~mm}\) is filled with water. The maximum height to which the water can be filled without leakage is (S.T. of water \(=[(75\) dyne \(\left.\\} / \mathrm{cm}], \mathrm{g}=1000 \mathrm{~m} / \mathrm{s}^{2}\right)\) (A) \(100 \mathrm{~cm}\) (B) \(75 \mathrm{~cm}\) (C) \(50 \mathrm{~cm}\) (D) \(30 \mathrm{~cm}\)

In a capillary tube water rises by \(1.2 \mathrm{~mm}\). The height of water that will rise in another capillary tube having half the radius of the first is (A) \(1.2 \mathrm{~mm}\) (B) \(2.4 \mathrm{~mm}\) (C) \(0.6 \mathrm{~mm}\) (D) \(0.4 \mathrm{~mm}\)

Water raises in a vertical capillary tube upto a height of \(2.0\) \(\mathrm{cm}\). If tube is inclined at an angle of \(60^{\circ}\) with the vertical then the what length the water will rise in the tube. (A) \(2.0 \mathrm{~cm}\) (B) \(4.0 \mathrm{~cm}\) (C) \((4 / \sqrt{3}) \mathrm{cm}\) (D) \(2 \sqrt{2} \mathrm{~cm}\)

A large number of water drops each of radius \(r\) combine to have a drop of radius \(\mathrm{R}\). If the surface tension is \(\mathrm{T}\) and the mechanical equivalent at heat is \(\mathrm{J}\) then the rise in temperature will be (A) \((2 \mathrm{~T} / \mathrm{rJ})\) (B) \((3 \mathrm{~T} / \mathrm{RJ})\) (C) \((3 \mathrm{~T} / \mathrm{J})\\{(1 / \mathrm{r})-(1 / \mathrm{R})\\}\) (D) \((2 \mathrm{~T} / \mathrm{J})\\{(1 / \mathrm{r})-(1 / \mathrm{R})\\}\)

When liquid medicine of density \(\mathrm{S}\) is to be put in the eye. It is done with the help of a dropper as the bulb on the top of the dropper is pressed a drop forms at the opening of the dropper we wish to estimate the size of the drop. We dirst assume that the drop formed at the opening is spherical because the requires a minimum increase in its surface energy. To determine the size we calculate the net vertical force due to surface tension \(\mathrm{T}\) when the radius of the drop is \(\mathrm{R}\). When this force becomes smaller than the weight of the drop the drop gets detached from the dropper. If \(\mathrm{r}=5 \times 10^{-4} \mathrm{~m}, \mathrm{p}=10^{3} \mathrm{~kg} \mathrm{~m}^{-3}=10 \mathrm{~ms}^{-2} \mathrm{~T}=0.11 \mathrm{~N} \mathrm{~m}^{-1}\) the radius of the drop when it detaches from the dropper is approximately (A) \(1.4 \times 10^{-3} \mathrm{~m}\) (B) \(3.3 \times 10^{-3} \mathrm{~m}\) (C) \(2.0 \times 10^{-3} \mathrm{~m}\) (D) \(4.1 \times 10^{-3} \mathrm{~m}\)

Read the assertion and reason carefully and mark the correct option given below. (a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is true but reason is false. (d) If the assertion and reason both are false. Assertion: When height of a tube is less then liquid rise in the capillary tube the liquid does not overflow. Reason: Product of radius of meniscus and height of liquid incapilling tube always remains constant. (A) a (B) \(b\) (C) c (D) d

Read the assertion and reason carefully and mark the correct option given below. (a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is true but reason is false. (d) If the assertion and reason both are false. Assertion: The concept of surface tension is held only for liquids. Reason: Surface tension does not hold for gases. (A) a (B) \(b\) (C) \(\mathrm{c}\) (D) \(\mathrm{d}\)

Read the assertion and reason carefully and mark the correct option given below. (a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is true but reason is false. (d) If the assertion and reason both are false. Assertion: The water rises higher in a capillary tube of small diametre than in the capillary tube of large diameter. Reason: Height through which liquid rises in a capillary tube is inversely proportional to the diameter of the capillary tube. (A) a (B) b (C) c (D) d

Read the assertion and reason carefully and mark the correct option given below. (a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is true but reason is false. (d) If the assertion and reason both are false. Assertion: Tiny drops of liquid resist deforming forces better than bigger drops. Reason: Excess pressure inside a drop is directly proportional to surface tension. (A) a (B) \(b\) (C) (D) d

A triangular lamina of area \(\mathrm{A}\) and, height \(\mathrm{h}\) is immersed in a liquid of density \(\mathrm{S}\) in a vertical plane with its base on the surface of the liquid. The thrust on lamina is (A) \((1 / 2)\) Apgh (B) \((1 / 3)\) Apgh (C) \((1 / 6)\) Apgh (D) \((1 / 3)\) Apgh

The density \(\rho\) of coater of bulk modulus \(B\) at a depth \(y\) in the ocean is related to the density at surface \(\rho_{0}\) by the relation. (A) \(\rho=\rho_{0}\left[1-\left\\{\left(\rho_{0} \mathrm{gy}\right\\} / \mathrm{B}\right\\}\right]\) (B) \(\rho=\rho_{0}\left[1+\left\\{\left(\rho_{0} \mathrm{gy}\right\\} / \mathrm{B}\right\\}\right]\) (C) \(\rho=\rho_{0}\left[1+\left\\{\left(\rho_{0} \mathrm{gyh}\right\\} / \mathrm{B}\right\\}\right]\) (D) \(\rho=\rho_{0}\left[1-\left\\{\mathrm{B} /\left(\rho_{0} \mathrm{~g} \mathrm{y}\right\\}\right]\right.\)

By sucking through a straw, a student can reduce the pressure in his lungs to \(750 \mathrm{~mm}\) of \(\mathrm{Hg}\) (density \(\left.=13.6\left(\mathrm{gm} / \mathrm{cm}^{2}\right)\right)\) using the straw, he can drink water from \(\mathrm{a}\) glass up to a maximum depth of (A) \(10 \mathrm{~cm}\) (B) \(75 \mathrm{~cm}\) (C) \(13.6 \mathrm{~cm}\) (D) \(1.36 \mathrm{~cm}\)

The fraction of floating object of volume \(\mathrm{V}_{0}\) and density \(\mathrm{d}_{0}\) above the surface of a Liquid as density \(\mathrm{d}\) will be (A) \(\left(\mathrm{d}_{0} / \mathrm{d}\right)\) (B) \(\left[\left\\{\mathrm{dd}_{0}\right\\} /\left\\{\mathrm{d}+\mathrm{d}_{0}\right\\}\right]\) (C) \(\left[\left\\{d-d_{0}\right\\} / d\right]\) (D) \(\left[\left\\{\mathrm{dd}_{0}\right\\} /\left\\{\mathrm{d}-\mathrm{d}_{0}\right\\}\right]\)

A body floats in water with one-third of its volume above the surface of water. It is placed in oil it floats with half of: Its volume above the surface of the oil. The specific gravity of the oil is. (A) \((5 / 3)\) (B) \((4 / 3)\) (C) \((3 / 2)\) (D) 1

A piece of solid weighs \(120 \mathrm{~g}\) in air, \(80 \mathrm{~g}\) in water and \(60 \mathrm{~g}\) in liquid the relative density of the solid and that of the solid and that of the liquid are respectively. (A) 3,2 (B) \(2,(3 / 4)\) (C) \((3 / 4), 2\) (D) \(3,(3 / 2)\)

Ice pieces are floating in a beaker A containing water and also in a beaker B containing miscible liquid of specific gravity \(1.2\) Ice melts the level of (A) water increases in \(\mathrm{A}\) (B) water decreases in \(\mathrm{A}\) (C) Liquid in B decrease B (D) Liquid in B increase

An engine pumps water continuously through a hose water leares the hose with a velocity \(\mathrm{V}\) and \(\mathrm{m}\) is the mass per unit length of the water Jet what is the rate at which kinetic energy is imparted to water. (A) \((1 / 2) \mathrm{mV}^{3}\) (B) \(\mathrm{mV}^{3}\) (C) \((1 / 2) \mathrm{mV}^{2}\) (D) \((1 / 2) \mathrm{mV}^{\alpha} \mathrm{V}^{2}\)

Eight drops of a liquid of density 3 and each of radius a are falling through air with a constant velocity \(3.75 \mathrm{~cm} \mathrm{~S}^{1}\) when the eight drops coalesce to form a single drop the terminal velocity of the new drop will be (A) \(15 \times 10^{-2} \mathrm{~ms}^{-1}\) (B) \(2.4 \times 10^{-2} \mathrm{~m} / \mathrm{s}\) (C) \(0.75 \times 10^{-2} \mathrm{~ms}^{-1}\) (D) \(25 \times 10^{-2} \mathrm{~m} / \mathrm{s}\)

Two drops of the same radius are falling through air with a steady velocity for \(5 \mathrm{~cm}\) per sec. If the two drops coakesce the terminal velocity would be (A) \(10 \mathrm{~cm}\) per sec (B) \(2.5 \mathrm{~cm}\) per sec (C) \(5 \times(4)^{(1 / 3)} \mathrm{cm}\) per sec (D) \(5 \times \sqrt{2} \mathrm{~cm}\) per sec

A tank is filled with water up to a height \(\mathrm{H}\). Water is allowed to come out of a hole P in one of the walls at a depth \(\mathrm{D}\) below the surface of water express the horizontal distance \(\mathrm{x}\) in terms of \(\mathrm{H}\) and \(\mathrm{D}\). (B) \(\left.\mathrm{x}={ }^{\alpha} \sqrt{[}\\{\mathrm{D}(\mathrm{H}-\mathrm{D})\\} / 2\right]\) (D) \(\mathrm{x}=4[\mathrm{D}(\mathrm{H}-\mathrm{D})]\)

An incompressible fluid flows steadily through a cylindrical pipe which has radius \(2 \mathrm{r}\) at point \(\mathrm{A}\) and radius \(\mathrm{r}\) at \(\mathrm{B}\) further along the flow direction. It the velocity at point \(\mathrm{A}\) is \(\mathrm{V}\), its velocity at point \(\mathrm{B}\). (A) \(2 \mathrm{~V}\) (B) V (C) \((\mathrm{V} / 2)\) (D) \(4 \mathrm{~V}\)

Two solid spheres of same metal but of mass \(\mathrm{M}\) and \(8 \mathrm{M}\) full simultaneously on a viscous liquid and their terminal velocity are \(\mathrm{V}\) and ' \(\mathrm{nV}^{\prime}\) then value of 'n' is (A) 16 (B) 8 (C) 4 (D) 2

Water is flowing continuously from a tap having an internal diameter \(8 \times 10^{-3} \mathrm{~m}\). The water velocity as it leaves the tap is \(0.4 \mathrm{~m} / \mathrm{s}\). The diameter of the water stream at a distance \(2 \times 10^{-1} \mathrm{~m}\) below the tap is close to (A) \(5.0 \times 10^{-3} \mathrm{~m}\) (B) \(7.5 \times 10^{-3} \mathrm{~m}\) (C) \(9.6 \times 10^{-3} \mathrm{~m}\) (D) \(3.6 \times 10^{-3} \mathrm{~m}\)

Oxygen boils at \(183^{\circ} \mathrm{C}\). This temperature is approximately. (A) \(215^{\circ} \mathrm{F}\) (B) \(-297^{\circ} \mathrm{F}\) (C) \(329^{\circ} \mathrm{F}\) (D) \(361^{\circ} \mathrm{F}\)

The resistance of a resistance thermometer has values \(2.71\) and \(3.70 \mathrm{ohm}\) at \(10^{\circ} \mathrm{C}\) and \(100^{\circ} \mathrm{C}\). The temperature at which the resistance is \(3.26 \mathrm{ohm}\) is (A) \(40^{\circ} \mathrm{C}\) (B) \(50^{\circ} \mathrm{C}\) (C) \(60^{\circ} \mathrm{C}\) (D) \(70^{\circ} \mathrm{C}\)

Maximum density of \(\mathrm{H}_{2} \mathrm{O}\) is at the temperature. (A) \(32^{\circ} \mathrm{F}\) (B) \(39.2^{\circ} \mathrm{F}\) (C) \(42^{\circ} \mathrm{F}\) (D) \(4^{\circ} \mathrm{F}\)

At what temperature the centigrade (celsius) and Fahrenheit readings at the same. \((\mathrm{A})-40^{\circ}\) (B) \(+40^{\circ} \mathrm{C}\) (C) \(36.6^{\circ}\) (D) \(-37^{\circ} \mathrm{C}\)

Mercury thermometers can be used to measure temperatures up to (A) \(100^{\circ} \mathrm{C}\) (B) \(212^{\circ} \mathrm{C}\) (C) \(360^{\circ} \mathrm{C}\) (D) \(500^{\circ} \mathrm{C}\)

If temperature of an object is \(140^{\circ} \mathrm{F}\) then its temperature in centigrade is (A) \(105^{\circ} \mathrm{C}\) (B) \(32^{\circ} \mathrm{C}\) (C) \(140^{\circ} \mathrm{C}\) (D) \(60^{\circ} \mathrm{C}\)

When the room temperature becomes equal to the dew point the relative humidity of the room is (A) \(100 \%\) (B) \(0 \%\) (C) \(70 \%\) (D) \(85 \%\)

If the length of a cylinder on heating increases by \(2 \%\) the area of its base will increase by. (A) \(0.5 \%\) (B) \(2 \%\) (C) \(1 \%\) (D) \(4 \%\)

A beaker is completely filled with water at \(4^{\circ} \mathrm{C}\) It will overflow if (A) Heated above \(4^{\circ} \mathrm{C}\) (B) Cooled below \(4^{\circ} \mathrm{C}\) (C) Both heated and cooled above and below \(4^{\circ} \mathrm{C}\) respectively (D) None of these

An iron bar of length \(10 \mathrm{~m}\) is heated from \(0^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C}\). If the coefficient of linear thermal expansion of iron is \(\left[\left\\{10 \times 10^{-6}\right\\} / \mathrm{C}\right]\) the increase in the length of bar is (A) \(0.5 \mathrm{~cm}\) (B) \(1.0 \mathrm{~cm}\) (C) \(1.5 \mathrm{~cm}\) (D) \(2.0 \mathrm{~cm}\)

Melting point of ice (A) Increases with increasing pressure (B) Decreases with increasing pressure (C) Is independent of pressure (D) is proportional of pressure

Amount of heat required to raise the temperature of a body through \(1 \mathrm{k}\) is called it is (A) Water equivalent (B) Thermal capacity (C) Entropy (D) Specific heat

A vessel contains \(110 \mathrm{~g}\) of water the heat capacity of the vessel is equal to \(10 \mathrm{~g}\) of water. The initial temperature of water in vessel is \(10^{\circ} \mathrm{C}\) If \(220 \mathrm{~g}\) of hot water at \(70^{\circ} \mathrm{C}\) is poured in the vessel the Final temperature neglecting radiation loss will be (A) \(70^{\circ} \mathrm{C}\) (B) \(80^{\circ} \mathrm{C}\) (C) \(60^{\circ} \mathrm{C}\) (D) \(50^{\circ} \mathrm{C}\)