A streamlined body falls through air from a height h on the surface of a liquid. If d and D(D > d) represents the densities of the material of the body and liquid respectively, then the time after which the body will be instantaneously at rest, is
1. √2hg
2. √2hg·Dd
3. √2hg·dD
4. √2hg(dD-d)
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 T1 to decrease the height of water to Hη(η>1) ; and it takes T2 time to take out the rest of water. If T1=T2, then the value of η is
1. 2
2. 3
3. 4
4. 2√2
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. ∝√h
2. ∝h
3. ∝(1/h)
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 V=πQPr4ηl where η is coefficient of the viscosity and Q is-
1. 8
2. 18
3. 16
4. 116
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. 4Q
2. Q
3. Q4
4. Q8
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 ρ and σ respectively, and the viscosity of the liquid is η).
1. r2g9η(ρ-2σ)
2. r2g9η(2ρ-σ)
3. r2g9η(ρ-σ)
4. 2r2g9η(ρ-σ)
An incompressible fluid flows steadily through a cylindrical pipe which has a radius 2r at the point A and a radius r at the point B further along the flow direction. If the velocity at the point A is v, its velocity at the 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 P0. Then density D of solid is given by
1. 54d
2. 45d
3. d
4. d5