$A$ small circular loop of area $A$ and resistance $R$ is fixed on a horizontal $xy$-plane with the center of the loop always on the axis $\hat{n}$ of a long solenoid. The solenoid has $m$ turns per unit length and carries current $I$ counterclockwise as shown in the figure. The magnetic field due to the solenoid is in $\hat{n}$ direction. $List-I$ gives time dependences of $\hat{n}$ in terms of a constant angular frequency $\omega$. $List-II$ gives the torques experienced by the circular loop at time $t=\frac{\pi}{6\omega}$. Let $\alpha=\frac{A^2 \mu_0^2 m^2 I^2 \omega}{2R}$.

$List-I$	$List-II$
$(I)$ $\frac{1}{\sqrt{2}}(\sin \omega t \hat{j}+\cos \omega t \hat{k})$	$(P)$ $0$
$(II)$ $\frac{1}{\sqrt{2}}(\sin \omega t \hat{i}+\cos \omega t \hat{j})$	$(Q)$ $-\frac{\alpha}{4} \hat{i}$
$(III)$ $\frac{1}{\sqrt{2}}(\sin \omega t \hat{i}+\cos \omega t \hat{k})$	$(R)$ $\frac{3\alpha}{4} \hat{i}$
$(IV)$ $\frac{1}{\sqrt{2}}(\cos \omega t \hat{j}+\sin \omega t \hat{k})$	$(S)$ $\frac{\alpha}{4} \hat{j}$

Which one of the following options is correct?

• A
  $I \rightarrow Q, II \rightarrow P, III \rightarrow S, IV \rightarrow R$
• B
  $I \rightarrow S, II \rightarrow T, III \rightarrow Q, IV \rightarrow P$
• C
  $I \rightarrow Q, II \rightarrow P, III \rightarrow S, IV \rightarrow R$
• D
  $I \rightarrow T, II \rightarrow Q, III \rightarrow P, IV \rightarrow R$