A thin uniform rod of length ' $L$ ' and mass ' $M$ ' is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ' $\omega$ '. Its centre of mass rises to a maximum height of

( $\mathrm{g}=$ acceleration due gravity)

In a biprism experiment a steady interference pattern is observed on the screen using a light of wavelength $5000 \mathop {\rm{A}}\limits^{\rm{o}}$. Without disturbing the set up of the experiment, the source of light is replaced by a source of wavelength $6400 \mathop {\rm{A}}\limits^{\rm{o}}$.

The fringe width will

Two girls are standing at the ends ' $A$ ' and ' $B$ ' of a ground where $\mathrm{AB}=\mathrm{b}$. The girl at ' B ' starts running in a direction perpendicular to ' $A B$ ' with velocity ' $\mathrm{V}_1$ '. The girl at ' A ' starts running simultaneously with velocity ' $\mathrm{V}_2$ ' and in shortest distance meets the other girl in time ' $t$ '. The value of ' $t$ ' is

A coil of wire of radius ' $r$ ' has 600 turns and a self-inductance of 108 mH . The self-inductance of a coil with same radius and 500 turns is