A thin metal wire of length ' L ' and mass ' M ' is bent to form semicircular ring as shown. The moment of inertia about $\mathrm{XX}^{\prime}$ is

A particle executes S.H.M. starting from the mean position. Its amplitude is ' a ' and its periodic time is ' $T$ '. At a certain instant, its speed ' $u$ ' is half that of maximum speed $\mathrm{V}_{\text {max }}$. The displacement of the particle at that instant is

Initially $n$ identical capacitors are joined in parallel and are charged to potential V. Now they are separated and joined in series. Then

When the electron orbiting in hydrogen atom goes from one orbit to another orbit (principal quantum number $=n$ ), the de-Broglie wavelength ( $\lambda$ ) associated with it is related to $n$ as