Physics

Figure A and B show long straight wires of circular cross section (a and b with a < b), carrying current I which is uniformly distributed across the cross section. The magnitude of magnetic field B varies with radius r and can be represented as:

A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical through its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is :
[Density of water ρw = 1000 kg m⁻³, and Density of air ρa = 1.2 kg m⁻³, g = 10 m/s², Coefficient of viscosity of air η = 1.8 * 10⁻⁵ Nsm⁻²]

The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 * 10³ km. Find the mass of Mars.
{Given 4π²/G = 6 * 10¹¹ N⁻²kg²}

The nuclear activity of a radioactive element becomes (1/8)ᵗʰ of its initial value in 30 years. The half –life of radioactive element is __________ years.

In a semiconductor, the number density of intrinsic charge carriers at 27°C is 1.5 * 10¹? / m³. If the semiconductor is doped with impurity atom, the hole density increases to 4.5*10²² / m³. The electron density in the doped semiconductor is __________ x 10? / m³.

A system consists of two types of gas molecules A and B having same number density 2*10²⁵ / m³. The diameter of A and B are 10 Å and 5 Å respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collision is __________ x10⁻².

A message single of frequency 20 kHz and peak voltage of 20 volt is used to modulate a carrier wave of frequency 1 MHz and peak voltage of 20 volt. The modulation index will be __________.

A light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV, placed in a magnetic field of intensity B. The electrons emitted perpendicular to the magnetic field B, with maximum kinetic energy are bent into circular arc of radius 30cm. The value of B is __________ x x 10⁻⁷ T
Given hc = 20 * 10?²? J-m, mass of electron = 9 * 10⁻³¹ kg

Two circuits are shown in the figure (a) & (b). At a frequency of __________ rad /s the average power dissipated in one cycle will be same in both the circuits.

A radioactive sample has an average life of 30ms and is decaying. A capacitor of capacitance 200 µF is first charged and later connected with resistor 'R'. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of 'R' should be _______ Ω.