Water is flowing in a pipe of diameter 4 cm with a velocity 3 m/s. The water then enters into a tube of diameter 2 cm. The velocity of water in the other pipe is
(1) 3 m/s
(2) 6 m/s
(3) 12 m/s
(4) 8 m/s
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 and respectively, and the viscosity of the liquid is ).
(1)
(2)
(3)
(4)
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. \(4v\)
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 . Then density D of solid is given by
(1)
(2)
(3)
(4)
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 |
A block of ice floats on a liquid of density 1.2 in a beaker. Then level of liquid when ice completely melts-
(1) Remains same
(2) Rises
(3) Lowers
(4) (a), (b) or (c)
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 to will be
(1)
(2)
(3)
(4)
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
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
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 -