Physics

Two Carnot engines A and B operate in series such that engine A absorbs heat at T? and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at T?. When work done in both the cases is equal, the value of T is:

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27°C to 37°C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? [R = 8.314 J mol⁻¹K⁻¹]

Match List I with List II.

 

Consider the following statements:
(A) Atoms of each element emit characteristics spectrum.
(B) According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit.
(C) The density of nuclear matter depends on the size of the nucleus.
(D) A free neutron is stable but a free proton decay is possible.
(E) Radioactivity is an indication of the instability of nuclei.
Choose the correct answer from the options given below:

Two identical particles of mass 1 kg each go round a circle of radius R, under the action of their mutual gravitational attraction. The angular speed of each particle is:

The resistance of a conductor at 15°C is 16Ω and at 100°C is 20Ω. What will be the temperature coefficient of resistance of the conductor?

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.