Q. No.Two non-mixing liquids of densities \(\rho\) and \(n\rho\) \((n>1)\) are put in a container. The height of each liquid is \(h.\) A solid cylinder of length \(L\) and density \(d\) is put in this container. The cylinder floats with its axis vertical and length \(rL~(r<1))\) in the denser liquid. The density \(d\) is equal to:
1. \([2+(n+1)r ]\rho\)
2. \([2+(n-1)r] \rho\)
3. \([1+(n-1)r] \rho\)
4. \([1+(n+1)r ]\rho\)
| 1. | surface tension. |
| 2. | density. |
| 3. | angle of contact between the surface and the liquid. |
| 4. | viscosity. |
A liquid does not wet the solid surface if the angle of contact is:
1. equal to \(45^{\circ}\)
2. equal to \(60^{\circ}\)
3. greater then \(90^{\circ}\)
4. zero
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. \(1~\text{cm}\)
An incompressible fluid flows steadily through a cylindrical pipe which has a radius \(2r\) at the point \(A\) and a radius \(r\) at the point \(B\) further along the flow direction. If the velocity at the point \(A\) is \(v,\) its velocity at the point \(B\) is:
1. \(2v\)
2. \(v\)
3. \(v/2\)
4. \(4v\)
A capillary tube of radius \(r\) is immersed in water and water rises in it to a height \(h.\) The mass of the water in the capillary is \(5\) g. Another capillary tube of radius \(2r\) is immersed in water. The mass of water that will rise in this tube is:
| 1. | \(5.0\) g | 2. | \(10.0\) g |
| 3. | \(20.0\) g | 4. | \(2.5\) g |
| 1. | \(r^3\) | 2. | \(r^2\) |
| 3. | \(r^5\) | 4. | \(r^4\) |
| 1. | \(D\) | 2. | \(A\) |
| 3. | \(B\) | 4. | \(C\) |
The cylindrical tube of a spray pump has radius \(R,\) one end of which has \(n\) fine holes, each of radius \(r.\) If the speed of the liquid in the tube is \(v,\) then the speed of ejection of the liquid through the holes will be:
| 1. | \(\dfrac{vR^2}{n^2r^2}\) | 2. | \(\dfrac{vR^2}{nr^2}\) |
| 3. | \(\dfrac{vR^2}{n^3r^2}\) | 4. | \(\dfrac{v^2R}{nr}\) |
A tank is filled with water up to a height \(H.\) The water is allowed to come out of a hole \(P\) in one of the walls at a depth \(D\) below the surface of the water. The horizontal distance \({x}\) in terms of \(H\) and \({D}\) is:
1. \(x = \sqrt{D\left(H-D\right)}\)
2. \(x = \sqrt{\frac{D \left(H - D \right)}{2}}\)
3. \(x = 2 \sqrt{D \left(H-D\right)}\)
4. \(x = 4 \sqrt{D \left(H-D\right)}\)
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