Three liquids of densities (with ), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact obey:
1. | \(\frac{\pi}{2}>\theta_1>\theta_2>\theta_3 \geq 0\) |
2. | \(0 \leq \theta_1<\theta_2<\theta_3<\frac{\pi}{2}\) |
3. | \(\frac{\pi}{2}<\theta_1<\theta_2<\theta_3<\pi\) |
4. | \(\pi>\theta_1>\theta_2>\theta_3>\frac{\pi}{2}\) |
Two non-mixing liquids of densities and n(n>1) are put in a container. The height of each liquid is h. A solid cylinder floats with its axis vertical and length pL in the denser liquid. The density of the cylinder is d. The density d is equal to:
1. {2+(n+1)p}
2. {2+(n-1)p}
3. {1+(n-1)p}
4. {1+(n+1)p}
The approximate depth of an ocean is 2700 m. The compressibility of water is 45.4 x 10-11 Pa-1 and density of water is 103kg/m3. What fractional compression of water will be obtained at the bottom of the ocean?
(1)0.8x10-2
(2)1.0x10-2
(3)1.2x10-2
(4)1.4x10-2
A wind with speed \(40~\text{m/s}\) blows parallel to the roof of a house. The area of the roof is \(250~\text{m}^2\). Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be: \(\left(\rho_{\text{air}}= 1.2~\text{kg/m}^3 \right)\)
1. \(4.8\times 10^{5}~\text{N}, ~\text{downwards}\)
2. \(4.8\times 10^{5}~\text{N}, ~\text{upwards}\)
3. \(2.4\times 10^{5}~\text{N}, ~\text{upwards}\)
4. \(2.4\times 10^{5}~\text{N}, ~\text{downwards}\)
The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is v, then the speed of ejection of the liquid through the holes will be:
1. vR2/n2r2
2. vR2/nr2
3. vR2/n3r2
4. v2R/nr
The heart of a man pumps 5 L of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury is \(13.6\times 10^3\)kg/m3 and g =10 m/s2, then the power of heart in watt is:
1. 1.70
2. 2.35
3. 3.0
4. 1.50
Water rises to a height h in capillary tube . If the length of capillary tube above the surface of water is made less than h, then
(1) water rises upto the tip of capillary tube and then starts overflowing like a fountain
(2) water rises upto the top of capillary tube and stays there without overflowing
(3) water rises upto a point a little below the top and stays there
(4) water does not rise at all
A certain number of spherical drops of a liquid of radius r coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then:\(\text { Energy }=4 V T\left(\frac{1}{r}-\frac{1}{R}\right) \text { is released } \)
1. | Energy = \(4 V T\left(\frac{1}{r}-\frac{1}{R}\right)\) is released | 2. | Energy =\(3 V T\left(\frac{1}{r}+\frac{1}{R}\right)\) is released |
3. | Energy =\(3 V T\left(\frac{1}{r}-\frac{1}{R}\right)\) is released | 4. | Energy is neither released nor absorbed |
The wettability of a surface by a liquid depends primarily on
(1) viscosity
(2) surface tension
(3) density
(4) angle of contact between the surface and the liquid
An engine pumps water continuously through a hose. Water leaves the hose with a velocity \(v\) and \(m\) is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?
1.
2.
3.
4.