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Q. No.A water spray gun is attached a hose of cross sectional area \(30~\text{cm}^2.\) The gun comprises of \(10\) perforations each of cross sectional area of \(15~\text{mm}^{2}.\) If the water flows in the hose with the speed of \(50~\text{cm/s},\) calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)
1. \(100~\text{m/s}\)
2. \(10~\text{m/s}\)
3. \(1000~\text{m/s}\)
4. \(15\times 10^{2}~\text{m/s}\)
1. \(100~\text{m/s}\)
2. \(10~\text{m/s}\)
3. \(1000~\text{m/s}\)
4. \(15\times 10^{2}~\text{m/s}\)
Subtopic: Equation of Continuity |
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The surface tension of a soap bubble is \(0.03~\text{N/m}.\) The work done in increasing the diameter of bubble from \(2~\text{cm}\) is \(\alpha \pi \times 10^{-4} ~\text{J} .\) The value of \(\alpha\) is: (Take \(\pi =3.14\))
1. \(0.86\)
2. \(0.64\)
3. \(1.92\)
4. \(7.68\)
1. \(0.86\)
2. \(0.64\)
3. \(1.92\)
4. \(7.68\)
Subtopic: Surface Tension |
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If an air bubble of diameter \(2~\text{mm}\) rises steadily through a liquid of density \(200~\text{kg/m}^{3}\) at a rate of \(0.5 ~\text{cm/s},\) then the coefficient of viscosity of liquid is: (in Poise) (Take \(g = 10~\text{m/s}^{2}\))
1. \(0.88\)
2. \(8.8\)
3. \(88.8\)
4. \(0.088\)
1. \(0.88\)
2. \(8.8\)
3. \(88.8\)
4. \(0.088\)
Subtopic: Stokes' Law |
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A cylindrical vessel of \(40~\text{cm}\) radius is completely filled with water and its capacity is \(528~\text{dm}^3\) (dm : decimeter) The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at \(70~\text{cm}\) below the top of water level, then horizontal range of water falling on the ground in the beginning is: (in cm)
1. \(120 \sqrt{2} \)
2. \(140 \sqrt{2} \)
3. \(140 \sqrt{3} \)
4. \(120 \sqrt{3}\)
1. \(120 \sqrt{2} \)
2. \(140 \sqrt{2} \)
3. \(140 \sqrt{3} \)
4. \(120 \sqrt{3}\)
Subtopic: Bernoulli's Theorem |
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A liquid drop of diameter \(2~\text{mm}\) breaks into \(512\) droplets. The change in surface energy is \(\alpha\times10^{-6}~\text{J}\). The value of \(\alpha\) is: (take surface tension of liquid =\(~0.08~\text{N/m}\))
1. \(10\)
2. \(7\)
3. \(8\)
4. \(11\)
1. \(10\)
2. \(7\)
3. \(8\)
4. \(11\)
Subtopic: Surface Tension |
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A tub is filled with water and a wooden cube \(10\) cm \(\times10\) cm \(\times 10\) cm is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by \(3.87\) cm. The mass of the metal coin is: (in gram)
(Take water density as \(1~\text{g/cm}^3\) and density of wood as \(0.4~\text{g/cm}^3\))
1. \(387\)
2. \(400\)
3. \(240\)
4. \(300\)
(Take water density as \(1~\text{g/cm}^3\) and density of wood as \(0.4~\text{g/cm}^3\))
1. \(387\)
2. \(400\)
3. \(240\)
4. \(300\)
Subtopic: Archimedes' Principle |
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Eight mercury drops, each of radius \(r\), coalesce to form bigger drop. The surface energy released in this process is: (\(S\) is the surface tension of mercury).
1. \(8 \pi r^2 {S}\)
2. \(16 \pi r^2 S\)
3. \(64 \pi r^2 {S}\)
4. \(4 \pi r^2 S\)
1. \(8 \pi r^2 {S}\)
2. \(16 \pi r^2 S\)
3. \(64 \pi r^2 {S}\)
4. \(4 \pi r^2 S\)
Subtopic: Surface Tension |
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A liquid of density \(600~\text{kg/m}^3\) flowing steadily in a tube of varying cross-section. The cross-section at a point \(A\) is \(1.0~\text{cm}^2\) and that at \(B \) is \(20~\text{mm}^2\). Both the points \(A\) and \(B\) are in same horizontal plane, the speed of the liquid at \(A\) is \(\text{cm/s}\). The difference in pressure at \(A\) and \(B\) points is: (in Pa)
1. \(18\)
2. \(144\)
3. \(36\)
4. \(72\)
1. \(18\)
2. \(144\)
3. \(36\)
4. \(72\)
Subtopic: Equation of Continuity |
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A spherical liquid drop of radius \(R\) acquires the terminal velocity \(v_1\) when falls through a gas of viscosity \(\eta .\) Now the drop is broken into \(64\) indentical droplets and each droplets acquires terminal velocity \(v_2\) falling through the same gas. The ratio of terminal velocities \(v_1/v_2 \) is:
1. \(4\)
2. \(0.25\)
3. \(32\)
4. \(16\)
1. \(4\)
2. \(0.25\)
3. \(32\)
4. \(16\)
Subtopic: Stokes' Law |
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The surface tension of a soap solution is \(3.5\times 10^{-2}~\text{N/m} \). The work required to increase the radius of a soap bubble from \(1~\text{cm}\) to \(2~\text{cm}\) is \(\alpha\times10^{-6}~\text{J}\). The value of \(\alpha\) is:
\((\pi=22 / 7)\)
1. \(300\)
2. \(264\)
3. \(500\)
4. \(900\)
\((\pi=22 / 7)\)
1. \(300\)
2. \(264\)
3. \(500\)
4. \(900\)
Subtopic: Surface Tension |
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