A vessel completely filled with water has two holes ' P ' and ' Q ' at depths ' 2 h ' and ' 8 h ' from the top respectively. Hole ' P ' is square of side ' $a$ ' and hole ' $Q$ ' is a circle of radius ' $r$ '. The water flowing out per second from both the holes is same, then side ' $a$ ' of hole ' $P$ ' is

A wire of length ' $L$ ' carries a current ' $I$ '. If the wire is turned into a square coil of single turn, the maximum magnitude of the torque in a given magnetic field $(\overrightarrow{\mathrm{B}})$ is

A black body has maximum wavelength ' $\lambda_{\mathrm{m}}$ ' at temperature 2000 K . Its maximum wavelength at 3000 K will be

The moment of inertia of a thin uniform rod of mass ' $M$ ' and length ' $L$ ', about an axis perpendicular to length of the rod and at a distance ' $L / 4$ ' from one end is