Mechanical Prop...

In the experimental arrangement shown in figure, the areas of cross-section of the wide and narrow portions of the tube are 5 cm$$^{2}$$ and 2 cm$$^{2}$$ respectively. The rate of flow of water through the tube is 500 cm$$^{3}$$ s$$^{-1}$$. The difference of mercury levels in the U-tube is:

A square hole of side a is made at a depth $$h$$ below water surface and to the side of a water container another circular hole of radius $$r$$ is made to the same container at a depth of $$4h$$. It is found that volume flow rate of water through both the holes is found to be same then:

A cylinder of height $$20m$$ is completely filled with water. The velocity of efflux of water (in $$ms^{-1}$$) through a small hole on the side wall of the cylinder near its bottom is:

Two drops of small radius are falling in air with constant velocity $$5 cms^{-1}$$. If they coalesce, then the terminal velocity will be

The velocity head of a stream of water is 40 cm. Then, the velocity of flow of water is :

A tank with vertical walls is mounted so that its base is at a height $$H$$ above the horizontal ground. The tank is filled with water to a depth '$$h$$' . A hole is punched in the side wall of the tank at a depth ' $$x$$ ' below the water surface. To have maximum range of the emerging stream,the value of $$x$$ is

Two equal drops of water are falling through air with a steady velocity of $$10\ cm/s$$. If the drops recombine to form a single drop then the terminal velocity is:

Two hail stones with radii in the ratio of $$1:2$$ fall from a great height through the atmosphere. Then the ratio of their momenta after they have attained terminal velocity is

A vessel is filled with water and kerosene oil. The vessel has a small hole in the bottom.  Neglecting viscosity if the thickness of water layer is $$h_{1}$$ and kerosene layer is $$h_{2}$$ then the velocity $$v$$ of flow of water will be (Given : density of water is $$\rho _{1}$$ g/ cc and that of kerosene is $$\rho _{2}$$ g/cc, neglecting viscosity):

The area of cross-section of the two arms of a hydraulic press are 1 cm$$^{2}$$ and 10 cm$$^{2}$$ respectively(fig.). A force of 5 N is applied on the water in the thinner arm. What force should be applied on the water in the thicker arm so that the water may remain in equilibrium?