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 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

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 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. \(8.0~\text{Nm}^{-1}\)

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