A tank is filled with water up to a height \(\mathrm H.\) Water is allowed to come out of a hole \(\mathrm P\) in one of the walls at a depth \(\mathrm D\) below the surface of water. Express the horizontal distance \(\mathrm{x}\) in terms of \(\mathrm H\) and \(\mathrm {D}\text :\)
1.
2.
3.
4.
If the excess pressure inside a soap bubble is balanced by an oil column of height of \(2\) mm, then the surface tension of the soap solution will be: (radius of the soap bubble, \(r=1\) cm and density of oil, \(d=0.8\) gm/cm3)
1. \(3.9\) N/m
2.
3.
4. \(3.9\) dyne/m
If the surface tension of water is \(0.06\) N/m2, then the capillary rise in a tube of diameter \(1\) mm is: \((\theta = 0^{\circ})\)
1. \(1.22\)m
2. \(2.44\)cm
3. \(3.12\)cm
4. \(3.86\) cm
The pans of a physical balance are in equilibrium. If Air is blown under the right hand pan then the right hand pan will:
1. | Move up | 2. | Move down |
3. | Move erratically | 4. | Remain at the same level |
A spherical ball of radius \(r\) is falling in a viscous fluid of viscosity \(\eta\) with a velocity \(v.\) The retarding viscous force acting on the spherical ball is:
1. | inversely proportional to \(r\) but directly proportional to velocity \(v.\) |
2. | directly proportional to both radius \(r\) and velocity \(v.\) |
3. | inversely proportional to both radius \(r\) and velocity \(v.\) |
4. | directly proportional to \(r\) but inversely proportional to \(v.\) |
There is a hole in the bottom of a tank having water. If the total pressure at the bottom is \(3\) atm \((1~\text{atm}=10^5~\text{N}/\text{m}^2),\) then the velocity of water flowing from the hole is:
1. \(\sqrt{400}~~\text{m/s}\)
2. \(\sqrt{600}~~\text{m/s}\)
3. \(\sqrt{60}~~\text{m/s}\)
4. none of these
The following figure shows the flow of liquid through a horizontal pipe. Three tubes \(A,\) \(B\) and \(C\) are connected to the pipe. The radii of the tubes \(A,\) \(B\) and \(C\) at the junction are respectively \(2\) cm, \(1\) cm and \(2\) cm. It can be said that:
1. | The height of the liquid in the tube \(A\)is maximum. |
2. | The height of the liquid in the tubes \(A\)and \(B\) is the same. |
3. | The height of the liquid in all the three tubes is the same. |
4. | The height of the liquid in the tubes \(A\) and \(C\) is the same. |
A barometer kept in a stationary elevator reads 76 cm. If the elevator starts accelerating up, the reading will be:
1. | zero. | 2. | equal to 76 cm. |
3. | more than 76 cm. | 4. | less than 76 cm. |
The value of g at a place decreases by 2%. Then, the barometric height of mercury:
1. | increases by 2%. | 2. | decreases by 2%. |
3. | remains unchanged. | 4. | sometimes increases and sometimes decreases. |
The height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill. The ratio of density of mercury to that of air is . The height of the hill is:
1. | 250 m | 2. | 2.5 km |
3. | 1.25 km | 4. | 750 m |