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) $928$ $kg$ $m^{-3}$

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:

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 

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

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. $\frac{1}{2}m{v}^3$                                   

2. $m{v}^3$

3. $\frac{1}{2}m{v}^2$                                   

4. $\frac{1}{2}{m}^2{v}^2$

A small sphere of radius \(r\) falls from rest in a viscous liquid. As a result, heat is produced due to the viscous force. The rate of production of heat when the sphere attains its terminal velocity is proportional to:
1. \(r^3\)
2. \(r^2\)
3. \(r^5\)
4. \(r^4\)

A rectangular film of liquid is extended from \((4~\text{cm} \times 2~\text{cm})\) to \((5~\text{cm} \times 4~\text{cm}).\) If the work done is \(3\times 10^{-4}\) J, the value of the surface tension of the liquid is:
1. \(0.250\) Nm^-1
2. \(0.125\) Nm^-1
3. \(0.2\) Nm^-1
4. \(8.0\) Nm^-1

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 of length \(L\) and density \(d\) is put in this container. The cylinder floats with its axis vertical and length \(rL~(r<1))\) in the denser liquid. The density \(d\) is equal to:
1. \([2+(n+1)r ]\rho\)
2. \([2+(n-1)r] \rho\)
3. \([1+(n-1)r] \rho\)
4. \([1+(n+1)r ]\rho\)

Water rises to a height ‘h’ in the capillary tube. If the length of the capillary tube is made less than ‘h’, then,

1. Water rises up to the tip of the capillary tube and then starts overflowing like a fountain.

2. Water rises up to the top of the capillary tube and stays there without overflowing.

3. Water rises up to a point little below the top and stays there.

4. Water does not rise at all.