Current Electricity — Physics STD 12 Science — Question

Find the equivalent capacitance of the infinite ladder shown in figure between the points A and B.

A gas is taken along the path AB as shown in figure. If 70cal of heat is extracted from the gas in the process, calculate the change in the internal energy of the system.

Figure. shows a large closed cylindrical tank containing water. Initially the air trapped above the water surface has a height h₀ and pressure 2p₀ where p₀ is the atmospheric pressure. There is a hole in the wall of the tank at a depth h₁ below the top from which water comes out. A long vertical tube is connected as shown.

1. Find the height h₂ of the water in the long tube above the top initially.
2. Find the speed with which water comes out of the hole.
3. Find the height of the water in the long tube above the top when the water stops coming out of the hole.

For the same objective, find the ratio of the least separation between two points to be distinguished by a microscope for light of 5000A and electrons accelerated through 100V used as the illuminating substance.

Obtain an expression for induced electromotive force due to rotational motion of a disc in a uniform magnetic field.

A cylindrical vessel, whose diameter and height both are equal to 30cm, is placed on a horizontal surface and a small particle P is placed in it at a distance of 5.0cm from the centre. An eye is placed at a position such that the edge of the bottom is just visible. The particle P is in the plane of drawing. Up to what minimum height should water be poured in the vessel to make the particle P visible?

Given below are some famous numbers associated with electromagnetic radiations in different contexts in physics. State the part of the electromagnetic spectrum to which each belongs.

1. 21 cm (wavelength emitted by atomic hydrogen in interstellar space).
2. 1057 MHz (frequency of radiation arising from two close energy levels in hydrogen; known as Lamb shift).
3. 2.7 K [temperature associated with the isotropic radiation filling all space-thought to be a relic of the ‘big-bang’ origin of the universe].
4. 5890 Å - 5896 Å [double lines of sodium]
5. 14.4 keV [energy of a particular transition in ⁵⁷Fe nucleus associated with a famous high resolution spectroscopic method (Mössbauer spectroscopy)].