Q. No.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 \(3\times 10^{-4}~\text J,\) 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. \(8.0~\text{Nm}^{-1}\)
| 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.
\((\rho_{\text {air }}=1.2~\text{kg/m}^3)\)
| 1. | \(4 \times 10^5~\text N,\) downwards | 2. | \(4 \times 10^5~\text N,\) upwards |
| 3. | \(2.4 \times 10^5~\text N,\) upwards | 4. | \(2.4 \times 10^5~\text N,\) downwards |
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:
| 1. | the energy \(= 4{VT}\left( \frac{1}{{r}} - \frac{1}{{R}}\right)\) is released. |
| 2. | the energy \(={ 3{VT}\left( \frac{1}{{r}} + \frac{1}{{R}}\right)}\) is released. |
| 3. | the energy \(={ 3{VT}\left( \frac{1}{{r}} - \frac{1}{{R}}\right)}\) is released. |
| 4. | the energy is neither released nor absorbed. |
| 1. | surface tension. |
| 2. | density. |
| 3. | angle of contact between the surface and the liquid. |
| 4. | viscosity. |
| 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 \(g = 10~\text{m/s}^{2}\), the density of water \(= 10^{3}~\text{kg/m}^3\), the value of \(Z_0\) is:
1. \(0.5~\text{cm}\)
2. \(100~\text{cm}\)
3. \(10~\text{cm}\)
4. \(1~\text{cm}\)
Two small spherical metal balls, having equal masses, are made from materials of densities \(\rho_1\) and \(\rho_2\) such that \(\rho_1=8\rho_2\)
| 1. | \(\dfrac{79}{72}\) | 2. | \(\dfrac{19}{36}\) |
| 3. | \(\dfrac{39}{72}\) | 4. | \(\dfrac{79}{36}\) |
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