In a U-tube, as shown in the figure, the water and oil are in the left side and right side of the tube respectively. The height of the water and oil columns are \(15~\text{cm}\) and \(20~\text{cm}\) respectively. The density of the oil is:
\(\left[\text{take}~\rho_{\text{water}}= 1000~\text{kg/m}^{3}\right]\)
1. \(1200~\text{kg/m}^{3}\)
2. \(750~\text{kg/m}^{3}\)
3. \(1000~\text{kg/m}^{3}\)
4. \(1333~\text{kg/m}^{3}\)
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. | \(\dfrac{79}{36}\) |
The velocity of a small ball of mass m and density when dropped in a container filled with glycerin of density becomes constant after sometime. The viscous force acting on the ball in the final stage is:-
1.
2.
3.
4. mg
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. \(1~\text{cm}\)
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 \((g = 10~\text{m/s}^2),\) 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. \(2.23\times10^{-6}~\text{m}^{3}/\text{s}\)
1. | surface tension. |
2. | density. |
3. | angle of contact between the surface and the liquid. |
4. | viscosity. |
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. |
A wind with a speed of \(40~\text{m/s}\) blows parallel to the roof of a house. The area of the roof is \(250~\text{m}^2.\) Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be:
\((\rho_{\text {air }}=1.2~\text{kg/m}^3)\)
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
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. \(1.4\times 10^{-2}\)
The heart of a man pumps \(5~\text{L}\) of blood through the arteries per minute at a pressure of \(150~\text{mm}\) of mercury. If the density of mercury is \(13.6\times10^{3}~\text{kg/m}^{3}\) \(g = 10~\text{m/s}^2,\) then the power of the heart in watts is:
1. | \(1.70\) | 2. | \(2.35\) |
3. | \(3.0\) | 4. | \(1.50\) |