What is the velocity v of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body ? (The densities of metal and of liquid are ρ and σ respectively, and the viscosity of the liquid is η).

(1) r2g9ηρ-2σ                     

(2) r2g9η2ρ-σ

(3) r2g9ηρ-σ                       

(4) 2r2g9ηρ-σ

Subtopic:  Viscosity |
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An incompressible fluid flows steadily through a cylindrical pipe which has a radius \(2r\) at point \(A\) and a radius \(r\) at \(B\) further along the flow direction. If the velocity at point \(A\) is \(v,\) its velocity at point \(B\) is:
1. \(2v\)                               
2. \(v\)
3. \(v/2\)                            
4. \(4v\)

Subtopic:  Equation of Continuity |
 84%
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A homogeneous solid cylinder of length L(L<H/2) . Cross-sectional area A/5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L/4 in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure P0. Then density D of solid is given by

(1) 54d   
                 
(2) 45d

(3) d     
                   
(4) d5

Subtopic:  Archimedes' Principle |
 70%
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 A wooden block with a coin placed on its top, floats in water as shown in fig. The distance \(l\) and \(h\) are shown there. After some time the coin falls into the water. Then:
                      

1. \(l\) decreases and \(h\) increases
2. \(l\) increases and \(h\) decreases
3. Both \(l\) and \(h\) increase
4. Both \(l\) and \(h\) decrease
Subtopic:  Archimedes' Principle |
 59%
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A block of ice floats on a liquid of density 1.2 g/cm3 in a beaker. Then level of liquid when ice completely melts-

(1) Remains same                         

(2) Rises

(3) Lowers                                   

(4) (a), (b) or (c)

Subtopic:  Archimedes' Principle |
 51%
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A vessel of area of cross-section A has liquid to a height H. There is a hole at the bottom of vessel having area of cross-section a. The time taken to decrease the level from H1 to H2 will be

(1)Aa2gH1-H2             

(2) 2gh

(3) 2gh(H1-H2)                     

(4) Aag2H1-H2

Subtopic:  Bernoulli's Theorem |
 74%
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A lead shot of 1mm diameter falls through a long column of glycerine. The variation of its velocity v with distance covered is represented by

Subtopic:  Viscosity |
 75%
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Water flows through a frictionless duct with a cross-section varying as shown in fig. Pressure p at points along the axis is represented by

Subtopic:  Bernoulli's Theorem |
 75%
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From amongst the following curves, which one shows the variation of the velocity v with time t for a small sized spherical body falling vertically in a long column of a viscous liquid -

Subtopic:  Viscosity |
 76%
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A liquid does not wet the sides of a solid if the angle of contact is

(1) Zero                                     

(2) Obtuse (More than 90°)

(3) Acute (Less than 90°)           

(4) 90°

Subtopic:  Capillary Rise |
 78%
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