A U tube with both ends open to the atmosphere,is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is 

  

(a) $650$ $kg$ $m^{-3}$

(b) $425$ $kg$ $m^{-3}$

(c) $800$ $kg$ $m^{-3}$

(d) $928$ $kg$ $m^{-3}$

A rectangular film of liquid is extended from (4 cm$\times$ $2$ $\mathrm{cm}$) to \((4 ~\text{cm}\times 5 ~\text{cm})\). If the work done is $3\times {10}^{-4}$ J, the value of the surface tension of the liquid is: 

Three liquids of densities ${\rho }_1,$ ${\rho }_2$ $and$ $$ ${\rho }_3$ (with ${\rho }_1>{\rho }_2>{\rho }_3$), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact ${\theta }_1,{\theta }_2$ $and$ ${\theta }_3$ obey:

 Two non-mixing liquids of densities $\rho$ and n$\rho$(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 $\left(p<1\right)$ in the denser liquid. The density of the cylinder is d. The density d is equal to:

1. {2+(n+1)p}$\rho$             

2. {2+(n-1)p}$\rho$

3. {1+(n-1)p}$\rho$             

4. {1+(n+1)p}$\rho$

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 m/s blows parallel to the roof of a house. The area of the roof is 250 m². 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: (P_air =1.2 kg/m³)
1. 4.8x10⁵ N, downwards
2. 4.8x10⁵ N, upwards
3. 2.4x10⁵ N, upwards
4. 2.4x10⁵ N, 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:\(\text { Energy }=4 V T\left(\frac{1}{r}-\frac{1}{R}\right) \text { is released } \)