The function of time representing a simple harmonic motion with a period of $${\pi \over \omega }$$ is :

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $$\gamma$$ is the ratio of specific heats) :

A proton and an $$\alpha$$-particle, having kinetic energies K_p and K_$$\alpha$$ respectively, enter into a magnetic field at right angles.

The ratio of the radii of trajectory of proton to that of $$\alpha$$-particle is 2 : 1. The ratio of K_p : K_$$\alpha$$ is :

An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is S₁ and that of the other part is S₂. Given that S₁ > S₂. If the piston is removed then the total entropy of the system will be :