We have a jar filled with gas characterized by parameters $$\mathrm{P}, \mathrm{V}, \mathrm{T}$$ and another jar B filled with gas having parameters $$2 \mathrm{P}, \frac{\mathrm{V}}{4}, 2 \mathrm{~T}$$, where symbols have their usual meaning. The ratio of number of molecules in jar A to those in jar B is

Two spheres each of mass '$$M$$' and radius $$\frac{R}{2}$$ are connected at the ends of massless rod of length '$$2 R$$'. What will be the moment of inertia of the system about an axis passing through centre of one of the spheres and perpendicular to the rod?

If the potential difference used to accelerate electrons is doubled, by what factor does the de-Broglie wavelength associated with electrons change?

A simple harmonic progressive wave is represented by $$y=A \sin (100 \pi t+3 x)$$. The distance between two points on the wave at a phase difference of $$\frac{\pi}{3}$$ radian is