A large tank of cross-section area A is filled with water to a height H. A small hole of area 'a' is made at the base of the tank. It takes time to decrease the height of water to ; and it takes time to take out the rest of water. If , then the value of is
(a) 2 (b) 3
(c) 4 (d)
As the temperature of water increases, its viscosity
(1) Remains unchanged
(2) Decreases
(3) Increases
(4) Increases or decreases depending on the external pressure
A small drop of water falls from rest through a large height h in air; the final velocity is
(1)
(2)
(3)
(4) Almost independent of h
The rate of flow of liquid in a tube of radius r, length l, whose ends are maintained at a pressure difference P is where is coefficient of the viscosity and Q is-
(1) 8
(2)
(3) 16
(4)
Water flows in a streamlined manner through a capillary tube of radius a, the pressure difference being P and the rate of flow Q. If the radius is reduced to a/2 and the pressure increased to 2P, the rate of flow becomes
(1)
(2)
(3)
(4)
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 |