A body of mass ‘m’ is released from rest on an inclined plane in an elevator (moving up with acceleration a₀). Find the time taken by the body to reach the bottom of the inclined plane

If we observe from the lift frame of reference, there will be a pseudo force acting downwards of a magnitude F=ma 

So from F.B.D we get 
$\begin{array}{l}\mathrm{N}=\mathrm{mgcos}\mathrm{\alpha }+{\mathrm{ma}}_0\cos \alpha \\ \mathrm{mgsin}\mathrm{\alpha }+{\mathrm{ma}}_0\sin \mathrm{\alpha }=\mathrm{ma}\\ \mathrm{a}=\left({\mathrm{a}}_0+\mathrm{g}\right)\sin \mathrm{\alpha }\end{array}$

$\mathrm{L}=\frac{1}{2}\left({\mathrm{a}}_0+\mathrm{g}\right)\sin {\mathrm{\alpha t}}^2$

$\mathrm{t}=\sqrt{\frac{2\mathrm{L}}{\left({\mathrm{a}}_0+\mathrm{g}\right)\sin \mathrm{\alpha }}}$