Using the law of conservation of energy.

Answer

Hint . Consider the change in the kinetic and potential energies of the interacting bodies for any possible displacement (the principle of virtual displacements)

Explanation

Let the rod sink by a distance `Deltay` Then the wedge will shift a distance `Deltax` to the left. Evidently `Deltay = Deltax` tan `alpha` Since the motion takos place with zero initial velocity, it follows that
`Deltax=a_(x)t^2//2,v_(x)=alpha_xt, Deltat^2//2v_(y)=a_yt`
According to the law of conservation of energy, the decrease in the potential energy of the rod as it sinks is equal to the increase in the kinetic energies of the rod and of the wedge:
`m_2gDeltay=(m_2v_y^2)/2+(m_1v_x^2)/(2)`
Substituting the values of the displacements and the velocities we obtain
`m_2ga_y=m_2a_y^2+m_1a_x^2,a_y=a_xtanalpha`
from which we get
`a_x=(m_a"g" tanalpha)/(m_1+m_2tan^2alpha),a_y=(m_2"g"tan^2alpha)/(m_1+m_2tan^2alpha)`
The reaction is
`Q=(m_1alpha_x)/(sinalpha)=(m_1m_2gcosalpha)/(m_1cos^2alpha+m_2sin^2alpha)`