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 |
 78%
From NCERT
NEET - 2019
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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 of the water and oil columns are \(15~\text{cm}\) and \(20~\text{cm}\) respectively. The density of the oil is: \(\left[\text{take}~\rho_{\text{water}}= 1000~\text{kg/m}^{3}\right]\)

              
1. \(1200~\text{kg/m}^{3}\)
2. \(750~\text{kg/m}^{3}\)
3. \(1000~\text{kg/m}^{3}\)
4. \(1333~\text{kg/m}^{3}\)

Subtopic:  Pressure |
 86%
From NCERT
NEET - 2019
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An incompressible liquid travels as shown in the figure. The speed of the fluid in the lower branch will :

1. 1 m/s

2. 1.5 m/s

3. 2.25 m/s

4. 3 m/s

Subtopic:  Equation of Continuity |
 80%
From NCERT
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An ice block of volume 32π3cm3is placed in
gravity free space. When ice completely melts, then
its surface area - (Neglect difference in density of ice and water)

1. 4π cm2

2. 8π cm2

3. 16π cm2

4. π cm2

Subtopic:  Properties of Fluids |
 58%
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Two horizontal pipes have radii in ratio 1 : 2 and
lengths in ratio 1 : 2. Same viscous fluid flows at
same pressure difference in both the pipes. The flow
rates are in the ratio

1. 1 : 2

2. 1 : 4

3. 1 : 8

4. 1 : 16

Subtopic:  Types of Flows |
 60%
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1 m3 water is brought inside the lake up to 200 metres depth from the surface of the lake. What will be changed in the volume when the bulk modulus of elastically of water is 22000 atmosphere? 
(density of water is 1 × 103 kg/m3 atmosphere pressure = 105 N/m2 and g = 10 m/s2 )

1.  8.9 × 103 m3

2.  7.8 × 103 m3

3.  9.1 × 104 m3

4.  8.7 × 104 m3

Subtopic:  Properties of Fluids |
 65%
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A spherical solid ball of volume V is made of a material of density ρ1. It is falling through a liquid of density ρ1 (ρ2 < ρ1). Assume that the 
liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., Fviscous = kv2 (k > 0). The terminal 
speed of the ball is

1.  Vgρ1 - ρ2k  

2.  Vgρ1k  

3.  Vgρ1k  

4.  Vgρ1 - ρ2k

Subtopic:  Stokes' Law |
 74%
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If the terminal speed of a sphere of gold (density = 19.5 kg/m3) is 0.2 m/s in a viscous liquid (density = 1.5 kg/m3), find the terminal speed of a sphere of silver (density = 10.5 kg/m3) of the same size in the same liquid

1.  0.4 m/s 

2.  0.133 m/s

3.  0.1 m/s 

4.  0.2 m/s

Subtopic:  Stokes' Law |
 73%
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By sucking through a straw, a student can reduce the pressure in his lungs to 750 mm of Hg (density = 13.6 gm/cm3). Using the straw, he can drink water from a glass up to a maximum depth of :

1.  10 cm 

2.  75 cm

3.  13.6 cm 

4.  1.36 cm

Subtopic:  Properties of Fluids |
 56%
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Three liquids of densities \(d,\) \(2d\) and \(3d\) are mixed in equal proportions of weights. The relative density of the mixture is: 

1. \(11d \over 7\) 2. \(18d \over 11\)
3. \(13d \over 9\) 4. \(23d \over 18\)
Subtopic:  Properties of Fluids |
 74%
From NCERT
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