The approximate depth of an ocean is \(2700~\text{m}\). The compressibility of water is \(45.4\times10^{-11}~\text{Pa}^{-1}\) and the density of water is \(10^{3}~\text{kg/m}^3\). What fractional compression of water will be obtained at the bottom of the ocean?
1. \(0.8\times 10^{-2}\)
2. \(1.0\times 10^{-2}\)
3. \(1.2\times 10^{-2}\)
4. \(1.4\times 10^{-2}\)

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. ${\mathrm{r}}^3$

2. ${\mathrm{r}}^2$

3. ${\mathrm{r}}^4$

4. ${\mathrm{r}}^5$

A small hole of an area of cross-section \(2~\text{mm}^2\) is present near the bottom of a fully filled open tank of height \(2~\text{m}.\) Taking \((g = 10~\text{m/s}^2),\)${\mathrm{}}^{}$ the rate of flow of water through the open hole would be nearly:
1. \(6.4\times10^{-6}~\text{m}^{3}/\text{s}\)
2. \(12.6\times10^{-6}~\text{m}^{3}/\text{s}\)
3. \(8.9\times10^{-6}~\text{m}^{3}/\text{s}\)
4. \(2.23\times10^{-6}~\text{m}^{3}/\text{s}\)

A soap bubble, having a radius of \(1~\text{mm}\), is blown from a detergent solution having a surface tension of \(2.5\times 10^{-2}~\text{N/m}\)$$. The pressure inside the bubble equals at a point \(Z_0\) below the free surface of the water in a container. Taking \(g = 10~\text{m/s}^{2}\)${\mathrm{}}^{}$, the density of water \(= 10^{3}~\text{kg/m}^3\)${\mathrm{}}^{}$, the value of \(Z_0\) is:
1. \(0.5~\text{cm}\)
2. \(100~\text{cm}\)
3. \(10~\text{cm}\)
4. \(1~\text{cm}\)

The density of ice is x gm/cc and that of water is y gm/cc. What is the change in volume in cc, when m gm of ice melts?

1.  M(y-x)

2.  (y-x)/m

3.  mxy(x-y)

4.  m(1/y-1/x)

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 \(3\times 10^{-4}~\text J,\) then the value of the surface tension of the liquid is:
1. \(0.250~\text{Nm}^{-1}\)
2. \(0.125~\text{Nm}^{-1}\)
3. \(0.2~\text{Nm}^{-1}\)
4. \(8.0~\text{Nm}^{-1}\)

A body weighs 160 g in air, 130 g in water and 136 g in oil. The specific gravity of oil is
1. 0.2 

2. 0.6

3. 0.7 

4. 0.8

Three liquids of densities \(d,\) \(2d\) and \(3d\) are mixed in equal proportions of weights. The relative density of the mixture is: