$A$ ball rolls without slipping. The radius of gyration of the ball about an axis passing through its center of mass is $K$. If the radius of the ball is $R$,what fraction of its total energy is associated with its rotational kinetic energy?

Pure $Si$ at $500\, K$ has equal number of electron $(n_e)$ and hole $(n_h)$ concentrations of $1.5 \times 10^{16} \,m^{-3}$. Doping by indium increases $n_h$ to $4.5 \times 10^{22} \,m^{-3}$. The doped semiconductor is of

$100$ cells each of e.m.f. $5 \ V$ and internal resistance $1 \ \Omega$ are to be arranged so as to produce maximum current in a $25 \ \Omega$ resistance. Each row is to contain equal number of cells. The number of rows should be

$A$ uniform but time-varying magnetic field $B(t)$ exists in a circular region of radius $a$ and is directed into the plane of the paper,as shown. The magnitude of the induced electric field at point $P$ at a distance $r$ $(r > a)$ from the centre of the circular region:

The normal to the curve $x = a(1 + \cos \theta)$,$y = a \sin \theta$ at $\theta$ always passes through which fixed point?

The figure shows the cross-section of a long cylindrical conductor through which an axial hole of radius $r$ is drilled with its center at point $A$. $O$ is the center of the conductor. If an identical hole were to be drilled centered at point $B$ while maintaining the same current density,the magnitude of the magnetic field at $O$: