A raindrop of radius r has a terminal velocity v m/s in air. The viscosity of air is $\eta$ poise. The viscous force on it is F. If the radius of the drop be 2r and the drop falls with terminal velocity in the same air, the viscous force on it will be:

1. F

2. F/2

3. 4F

4. 8F

Assertion: A block of wood floats in a bucket of water in a lift. The block sink more if the lift starts accelerating up.

Reason: When lift is accelerating upward then weight is more than force of buoyancy.

If the Reynolds number of water flowing in a pipe in CGS units is 1000, then the Reynolds number of water in SI units will be :

1. ${10}^2$

2. ${10}^4$

3. ${10}^6$

4. ${10}^3$

A cylindrical vessel filled with water is released on an inclined surface of an angle $\theta$ as shown in the figure. The friction coefficient of the surface with the vessel is $\mu \left(<\tan \theta \right)$. Then the constant angle made by the surface of the water with the incline will be-

1. ${\tan }^{-1}\mu$

2. $\theta -{\tan }^{-1}\mu$

3. $\theta +{\tan }^{-1}\mu$

4. $co{t}^{-1}\mu$

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

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. \(2.23\times10^{-6}~\text{m}^{3}/\text{s}\)