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The blades of a windmill sweep out a circle of area A. If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it in time t?

$1.\mathrm{\rho Avt}$

$2.\frac{1}{2}\mathrm{\rho Avt}$

$3.2\mathrm{\rho Avt}$

$4.\frac{3}{2}\mathrm{\rho Avt}$

Subtopic: Equation of Continuity |

51%

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Bernoulli's theorem is applicable in the case of:

1. the compressible liquid in a streamlined flow.

2. the compressible liquid in a turbulent flow.

3. the incompressible liquid in a streamlined flow.

4. the incompressible liquid in a turbulent flow.

Subtopic: Bernoulli's Theorem |

69%

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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 \(70~\text{ms}^{-1}\)^{} and \(63~\text{ms}^{-1}\)^{ }respectively. What is the lift on the wing if its area is \(2.5~\text{m}^2\)? (Take the density of air to be \(1.3 ~\text{kg m}^{-3}\))

1. \(2.5\times 10^5~\text{N}\)

2. \(1.5\times 10^5~\text{N}\)

3. \(2.5\times 10^3~\text{N}\)

4. \(1.5\times 10^3~\text{N}\)

Subtopic: Bernoulli's Theorem |

56%

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The cylindrical tube of a spray pump has a cross-section of \(8.0\) cm^{2} one end of which has \(40\) fine holes each of diameter \(1.0\) mm. If the liquid flow inside the tube is \(1.5\) m-min^{–1}, the speed of ejection of the liquid through the holes is:

1. \(0.64\) ms^{-1}

2. \(0.74\) ms^{-1}

3. \(0.54\) ms^{-1}

4. \(0.84\) ms^{-1}

Subtopic: Equation of Continuity |

63%

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A U-shaped wire is dipped in a soap solution and removed. The thin soap film formed between the wire and the light slider supports a weight of \(1.5\times10^{-2}\) N (which includes the small weight of the slider). The length of the slider is \(30\) cm. The surface tension of the film is:

1. | \(3.5\times10^{-2}\) Nm^{–1} |
2. | \(2.5\times10^{-2}\) Nm^{–}^{1} |

3. | \(3.5\times10^{-3}\) Nm^{–}^{1} |
4. | \(2.5\times10^{-3}\) Nm^{–}^{1} |

Subtopic: Surface Tension |

76%

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What is the pressure inside the drop of mercury of radius 3.00 mm at room temperature? The surface tension of mercury at that temperature (${20}^{0}C$) is 4.65 × 10^{–1} N m^{–1}. The atmospheric pressure is 1.01 × 10^{5} Pa.

$\left(1\right)2.30\times {10}^{5}Pa$

$\left(2\right)2.01\times {10}^{5}Pa$

$\left(3\right)3.01\times {10}^{5}Pa$

$\left(4\right)1.01\times {10}^{5}Pa$

Subtopic: Surface Tension |

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Which one of the following is true from the given statements?

1. | Surface tension of liquids generally increases with temperatures. |

2. | Viscosity of gases decreases with temperature. |

3. | For solids with an elastic modulus of rigidity, the shearing force is proportional to the shear strain. |

4. | For the model of a plane in a wind tunnel, turbulence occurs at a smaller speed than turbulence for an actual plane. |

Subtopic: Properties of Fluids |

51%

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A \(50~\text{kg}\) girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter of \(1.0~\text{cm}\). What is the pressure exerted by the heel on the horizontal floor:

1. \( 6.24 \times 10^6 ~\text{Nm}^{-2} \)

2. \( 4.21 \times 10^5 ~\text{Nm}^{-2} \)

3. \( 20 \times 10^6 ~\text{Nm}^{-2}\)

4. \( 1.01 \times 10^5~\text{Nm}^{-2}\)

1. \( 6.24 \times 10^6 ~\text{Nm}^{-2} \)

2. \( 4.21 \times 10^5 ~\text{Nm}^{-2} \)

3. \( 20 \times 10^6 ~\text{Nm}^{-2}\)

4. \( 1.01 \times 10^5~\text{Nm}^{-2}\)

Subtopic: Pressure |

70%

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Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density \(984~\text{kg/m}^3.\) The height of the wine column for normal atmospheric pressure is:

1. \(11.5~\text{m}\)

2. \(10.5~\text{m}\)

3. \(9.00~\text{m}\)

4. \(15.0~\text{m}\)

Subtopic: Pressure |

70%

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A hydraulic automobile lift is designed to lift cars with a maximum mass of \(3000\) kg. The area of the cross-section of the piston carrying the load is \(425\) cm^{2}. What maximum pressure would the smaller piston have to bear?

1. \(3.12\times10^{5}\) Pa

2. \(1.01\times10^{5}\) Pa

3. \(2.94\times10^{5}\) Pa

4. \(6.92\times10^{5}\) Pa

Subtopic: Pressure |

79%

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