Three points masses, each of mass $m$ are placed at the corners of an equilateral triangle of side $\ell$. The moment of inertia of the system about an axis passing through one of the vertices and parallel to the side joining other two vertices, will be

Using Bohr's model, the orbital period of electron in hydrogen atom in $n$th orbit is ( $\varepsilon_0=$ permittivity of free space, $h=$ Planck's constant, $m=$ mass of electron and $\theta=$ electronic charge)

Let $\sigma$ and $b$ be Stefan's constant and Wien's constant respectively, then dimensions of $\sigma b$ are

At the poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting to produce resonance with same fork, the vibrating length of wire