A small circular loop of area \( A \) and resistance \( R \) is fixed on a horizontal \( xy \)-plane with the centre 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 \( t=\dfrac{\pi}{6\omega} \). Let \( \alpha=\dfrac{A^{2}\mu_{0}^{2}m^{2}I^{2}\omega}{2R} \).
Which one of the following options is correct?
