A non – conducting ring of radius R having uniformly distributed charge Q starts rotating about $\mathrm{X}\text{\hspace{0.17em}X'}$  axis passing through the  centre in the plane of the ring with an angular acceleration $\text{'}\alpha \text{'}$ as shown in the figure.  Another small conducting ring having radius $a(a<<R)$ is kept fixed at the centre of bigger ring in such a way that the axis  is passing through its centre and perpendicular to its plane.  If the resistance of the small ring is $r=1\Omega$, find the induced current in it (in ampere).

(Given  $Q=\frac{16\times {10}^2}{{\mu }_o}C,R=1\mathrm{m},a=0.1\mathrm{m},\alpha =8\mathrm{rad}/{\mathrm{s}}^{-2}$)