The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $\frac{\mathrm{d}}{2}$, then the viscous force acting on the ball will be:

1. $\frac{3}{2}\mathrm{Mg}$

2. 2Mg

3. $\frac{\mathrm{Mg}}{2}$

4. Mg

Subtopic: Viscosity |

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A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :

1. 5.0 g

2. 10.0 g

3. 20.0 g

4. 2.5 g

Subtopic: Capillary Rise |

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A liquid does not wet the solid surface if the angle of contact is:

1. equal to $45\xb0$

2. equal to $60\xb0$

3. greater then $90\xb0$

4. zero

Subtopic: Surface Tension |

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A barometer is constructed using a liquid ( density = $760\mathrm{kg}/{\mathrm{m}}^{3}$ ). What would be the height of the liquid column, when a mercury barometer reads 76 cm?

$(\mathrm{density}\mathrm{of}\mathrm{mercury}=13600\mathrm{kg}/{\mathrm{m}}^{3})$

1. 1.36 m

2. 13.6 m

3. 136 m

4. 0.76 m

Subtopic: Pressure |

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A small hole of an area of cross-section 2 $m{m}^{2}$ is present near the bottom of a fully filled open tank of height 2 m. Taking g= 10 $m/{s}^{2}$, the rate of flow of water through the open hole would be nearly:

1. $6.4\times {10}^{-6}{m}^{3}/s$

2. $12.6\times {10}^{-6}{m}^{3}/s$

3. $8.9\times {10}^{-6}{m}^{3}/s$

4. $2.23\times {10}^{-6}{m}^{3}/s$

Subtopic: Bernoulli's Theorem |

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A soap bubble, having a radius of 1 mm, is blown from a detergent solution having a surface tension of $2.5\times {10}^{-2}N/m$. The pressure inside the bubble equals at a point ${Z}_{0}$ below the free surface of the water in a container. Taking g= 10 m/${s}^{2}$, density of water = ${10}^{3}kg/{m}^{3}$, the value of ${Z}_{0}$ is:

1. 0.5 cm

2. 100 cm

3. 10 cm

4. 1 cm

Subtopic: Surface Tension |

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Two small spherical metal balls, having equal masses, are made from materials of densities ${\rho}_{1}and{\rho}_{2}$ such that ${\rho}_{1}=8{\rho}_{2}$ and having radii of 1 mm and 2 mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals $\eta $ and whose density is 0.1${\rho}_{2}$. The ratio of their terminal velocities would be:

1. $\frac{79}{72}$

2. $\frac{19}{36}$

3. $\frac{39}{72}$

4. $\frac{79}{36}$

Subtopic: Viscosity |

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In a U-tube, as shown in the figure, the water and oil are in the left side and right side of the tube respectively. The height for water and oil columns are 15 cm and 20 cm respectively. The density of the oil is: $[take{\rho}_{water}=1000kg/{m}^{3}]$

1. 1200 $kg/{m}^{3}$

2. 750 $kg/{m}^{3}$

3. 1000 $kg/{m}^{3}$

4. 1333 $kg/{m}^{3}$

Subtopic: Pressure |

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A small sphere of radius 'r' falls from rest in a viscous liquid. As a result, heat is produced due to the viscous force. The rate of production of heat when the sphere attains its terminal velocity is proportional to:

1. ${r}^{3}$

2. ${r}^{2}$

3. ${r}^{5}$

4. ${r}^{4}$

Subtopic: Stokes' Law |

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A U-tube with both ends open to the atmosphere is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a level of 10 mm above the water level on the other side. Meanwhile, the water rises by 65 mm from its original level (see diagram). The density of the oil is:

** **

1. 425 kg ${m}^{-3}$

2. 800 Kg ${m}^{-3}$

3. 928 Kg ${m}^{-3}$

4. 650 Kg ${m}^{-3}$

Subtopic: Pressure |

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