Wedge and rope

let the length of the left side be a and right side be b.

by triangle equality,
asinβ = bsinα = k(say)

so, a = k sinβ; b= ksinα; total length=k(sinα+sinβ)

let mass per unit length be x.

force down the plane in left = ksinβsinα
force down the plane in right = ksinαsinβ

Net force = 0

no accn.!

if for any shape the two ends of the rope are at same horizontal level, then the net accn is always ZERO!