Properties Of Matter - Mechanics - Physics Previous Year Questions

A U-tube is rotated about one of its limbs with an angular velocity \(\omega\). Find the difference in height \(\mathrm{H}\) of the liquid (density \(\rho\) ) level, where the diameter of the tube is \(d < <\mathrm{L}\).

Let the cylinder is prevented from moving up, by applying a force and water level is further decreased. Then, the height of water level ( $h_2$ in the figure) for which the cylinder remains in original position without application of force is

If the level of liquid starts decreasing slowly when the level of liquid is at a height $h_1$ above the cylinder, the block just starts moving up. Then, the value of $h_1$ is:

If the height $h_2$ of water level is further decreased, then

Column I gives some devices and Column II gives some process on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II and indicate your answer by darkening appropriate bubbles in the \(4 \times 4\) matrix given in the ORS.

Water is filled up to a height \(h\) in a beaker of radius \(R\) as shown in the figure. The density of water is \(\rho\), the surface tension of water is \(T\) and the atmospheric pressure is P. Consider a vertical section \(A B C D\) of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

STATEMENT - 1 :

The stream of water flowing at high speed from a garden hose pipe tends to spread line a fountain when held vertically up, but tends to narrow down when held vertically down.

and

STATEMENT - 2 :

In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)

When the gas bubble is at a height y from the bottom, its temperature is :

A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve,

Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m\(^2\). The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap-water used to make bubbles is 0.04 N/m. Find the ratio \(n_B/n_A\), where \(n_A\) and \(n_B\) are the number of moles of air in bubbles A and B, respectively. (Neglect the effect of gravity.)

A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice and the water level in the vessel becomes steady with height of water column being 200 mm. Find the fall in height (in mm) of water level due to opening of the orifice. (Take atmospheric pressure = 1.0 \(\times\) 10\(^5\) N/m\(^2\), density of water = 1000 kg/m\(^3\) and g = 10 m/s\(^2\). Neglect any effect of surface tension.)

After the drop detaches, its surface energy is

If the radius of the opening of the dropper is \(r\), the vertical force due to the surface tension on the drop of radius R (assuming \(r\) << R) is

If r = 5 \(\times\) 10⁻⁴ m, \(\rho\) = 10³ kg m⁻³ , g = 10 m/s² , T = 0.11 Nm⁻¹ , the radius of the drop when it detaches from the dropper is approximately

A composite block is made of slabs A, B, C, D and E of different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat Q flows only from left to right through the blocks. Then, in steady-state

Two solid spheres A and B of equal volumes but of different densities d_A and d_B are connected by a string. They are fully immersed in a fluid of density d_F. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if

A person blows into the open end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,