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Q. No.The surface tension of soapy water is \(S.\) When bubbles are blown with soapy water, one bubble of radius \(r\) is formed within another of radius \(3r.\) The excess pressure within the smaller bubble, relative to the atmospheric pressure is:
1.
\(\dfrac{4S}{r}\)
2.
\(\dfrac{8S}{3r}\)
3.
\(\dfrac{8S}{r}\)
4.
\(\dfrac{16S}{3r}\)
Subtopic: Surface Tension |
Level 3: 35%-60%
Hints
Consider a tank full of water with an outlet at the bottom. As the outlet valve is opened, and water flows out, the pressure inside the tank near the outlet:
| 1. | increases. |
| 2. | decreases. |
| 3. | remains unchanged. |
| 4. | increases and then quickly returns to normal. |
Subtopic: Pressure |
58%
Level 3: 35%-60%
Hints
Water flows from a small hole at the bottom of a rectangular tank at \(10\) m/s after it had been filled for \(20\) min. For how much time should the empty tank be filled at the same rate so that the speed of efflux is doubled? (i.e. it becomes \(20\) m/s)
1. \(40\) min
2. \(80\) min
3. \(160\) min
4. \(320\) min
1. \(40\) min
2. \(80\) min
3. \(160\) min
4. \(320\) min
Subtopic: Bernoulli's Theorem |
55%
Level 3: 35%-60%
Hints
A viscous liquid is flowing through a straight tube under the action of a pressure difference across the ends of the tube. The tube is aligned with the \(x\)-axis. The force exerted on the tube by the liquid has the form:
\((a,b>0)\)
\((a,b>0)\)
| 1. | \(a\hat i\) | 2. | \(-a\hat i\) |
| 3. | \(a\hat i+b\hat j\) | 4. | \(-a\hat i+b\hat j\) |
Subtopic: Viscosity |
Level 3: 35%-60%
Hints
A pair of soap bubbles cling together to form a double-bubble as shown: their respective radii are \(3R,R.\) The radius of their interface \((PQ)\) is:
| 1. | \(2R\) | 2. | \(5R\) |
| 3. | \(\dfrac{3R}{4}\) | 4. | \(\dfrac{3R}{2}\) |
Subtopic: Surface Tension |
59%
Level 3: 35%-60%
Hints
Water is under high pressure within a tank. When a hole is made at the top of the tank, a stream of water rises up vertically to a height \(H\) above the hole. Assume the flow to be streamlined. The water pressure (gauge pressure) at the top of the tank, initially, was: (\(\rho\) density of water)
| 1. | \(H\rho g\) | 2. | \(\dfrac{H\rho g}{2}\) |
| 3. | \(2 H\rho g\) | 4. | \(\sqrt 2 H \rho g\) |
Subtopic: Bernoulli's Theorem |
63%
Level 2: 60%+
Hints
A tank of uniform cross-section is filled with water. The pressure at the bottom of the tank is \( P_0,\) and the volume of water is \(V_0.\) Ignore atmospheric pressure. The potential energy of the water in the tank (taking the base as the reference) is:
| 1. | \( P_0V_0\) | 2. | \(2 P_0V_0\) |
| 3. | \({\Large\frac{ P_0V_0}2}\) | 4. | \({\Large\frac{ P_0V_0}4}\) |
Subtopic: Pressure |
52%
Level 3: 35%-60%
Hints
The bob (mass : \(m\)) of a simple pendulum is suspended from a long wire of length \(L.\) When this bob is submerged in a fluid of density \(\rho,\) it is observed by means of a careful measurement that the extension in the wire is halved. The volume of the bob is:
| 1. | \(\dfrac{m}{\rho}\) | 2. | \(\dfrac{2m}{\rho}\) |
| 3. | \(\dfrac{m}{2\rho}\) | 4. | \(\dfrac{3m}{2\rho}\) |
Subtopic: Archimedes' Principle |
60%
Level 2: 60%+
Hints
A liquid of density \(\rho\) flows through a bent tube of cross-section \(A,\) with a speed \(v.\) The liquid enters at point \(A\) and exits at \(B\) in the opposite direction. The radius of the bend is \(R.\) The tube lies on a horizontal table. The force required to hold the tube equals:
1. \(\rho Av^2\)
2. \(2\rho Av^2\)
3. \(\sqrt2\rho Av^2\)
4. \(\rho v^2\pi R^2\)
1. \(\rho Av^2\)
2. \(2\rho Av^2\)
3. \(\sqrt2\rho Av^2\)
4. \(\rho v^2\pi R^2\)
Subtopic: Pressure |
58%
Level 3: 35%-60%
Hints
A large vessel of liquid of density \(\rho\) is contained in a tank. The tank is pulled towards the right with a constant acceleration \(a.\) The upper level of the liquid is not shown in the diagram. Then, the pressures at \(A\) and \(B\) are related by:
1. \(P_A=P_B\)
2. \(P_A-P_B=L\rho a\)
3. \(P_B-P_A=L\rho a\)
4. \(P_A-P_B=L\rho \sqrt{a^2+g^2}\)
1. \(P_A=P_B\)
2. \(P_A-P_B=L\rho a\)
3. \(P_B-P_A=L\rho a\)
4. \(P_A-P_B=L\rho \sqrt{a^2+g^2}\)
Subtopic: Pressure |
52%
Level 3: 35%-60%
Hints
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