A non–conducting ring of radius $R$ having uniformly distributed charge $Q$ starts rotating about $\mathrm{x}–\mathrm{x}\mathrm{\text{'}}$ axis passing through diameter with an angular acceleration $\alpha$, as shown in the figure. Another small conducting ring having radius $a$ $\left(a\ll R\right)$ is kept fixed at the centre of the bigger ring is such a way that axis $\mathrm{xx}\mathrm{\text{'}}$ is passing through its centre and perpendicular to its plane. If the resistance of the small ring is $r=1 \mathrm{\Omega },$ find the induced current in it in $\mathrm{ampere}$.
(Given $q=\frac{16\times 10^2}{{\mu }_0} \mathrm{C},$ $R=1 \mathrm{m}, a = 0.1 \mathrm{m}$, $\alpha =8 \mathrm{r}\mathrm{a}\mathrm{d} {\mathrm{s}}^{-2}$)