Mechanical Prop...

Three capillaries of internal radii $$2r$$, $$3r$$ and $$4r$$, all of the same length, are joined end to end. A liquid passes through the combination and the pressure difference across this combination is $$20.2 cm$$ of mercury. The pressure difference across the capillary of internal radius $$2r$$ is

 A small hole is made at a height of $$h = \dfrac{1}{2}  m$$ from the bottom of a cylindrical water tank and at a depth of $$h = 2 m$$ from the upper level of water in the tank. The distance, where the water emerging from the hole strikes the ground, is:

If the terminal speed of a sphere of gold (density $$\displaystyle =19.5\quad { kg }/{ { m }^{ 3 } }$$) is $$\displaystyle 0.2{ m }/{ s }$$ in a viscous liquid (density $$\displaystyle =1.5\quad { kg }/{ { m }^{ 3 } }$$), find the terminal speed of a sphere of silver (density $$\displaystyle =10.5\quad { kg }/{ { m }^{ 3 } }$$) of the same size in the same liquid.

A tank is filled upto a height $$h$$ with a liquid and is placed on a platform of height $$h$$ from the ground. To get maximum range, $${x}_{m}$$ a small hole is punched at a distance of $$y$$ from the free surface of the liquid. Then

A wooden cylinder of diameter $$4r$$, height $$h$$ and density $$\rho /3$$ is kept on a hole of diameter $$2r$$ of a tank filled with water of density $$\rho$$ as shown in the figure. The height of the base of cylinder from the base of tank is $$H$$. Now level of the liquid starts decreasing slowly. When the level of the liquid is at a height $$h_1$$, above the cylinder the block just starts to lift. At what value of $${h}_{1}$$, will the block rise.

The block is maintained at the position by external means and the level of liquid is lowered. The height $${h}_{2}$$ when the external force reduces to zero is

Figure shows a crude type of atomizer. When bulb $$A$$ is compressed, air flows swiftly through tube $$BC$$ causing a reduced pressure in the particle of the vertical tube. Liquid rises in the tube, enters $$BC$$ and is sprayed out. If the pressure in the bulb is $${ P }_{ a }+P,$$ where $$P$$ is the gauge pressure and $${ P }_{ a }$$ is the atmosphere pressure, $$v$$ is the speed of air in $$BC$$. Density of air$$=1.3\ kg/{ m }^{ 3 }$$.

Two fully blown balloons are suspended as shown in the diagram. A stream of air is passed in between the balloons. What will happen to the balloons?

In the adjoining figure, the cross-sectional area of the smaller tube is a and the larger tube is 2a. A block of mass 2 m is kept in the smaller tube have the same base area an as that of the tube. The difference between water levels of the two tubes are (density of water is $$\rho$$ and in $${ \rho  }_{ 0 }$$ is atmospheric pressure)

A plane is in level flight at constant speed and each of its two wings has an area of 25 m$$^2$$. If the speed of the air on the upper and lower surfaces of the wing are 270 km h$$^{-1}$$ and 234 km h$$^{-1}$$ respectively, then the mass of the plane is (Take the density of the air = 1 kg m$$^{-3}$$)