A uniform rope of length L and mass M is placed on a smooth fixed wedge as shown. Both ends of rope are at same horizontal level. The rope is initially released from rest, then the magnitude of initial acceleration of rope is

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​ m 1 ​ = ( L III ​ ​ l 1 ​ , m 2 ​ = ( L III ​ ) l 2 ​ ​ sin α = l 1 ​ h ​ ​ h = l 1 ​ sin α = l 2 ​ sin β ​ ∵ l 1 ​ + l 2 ​ = L ​ l 1 ​ + sin β l 1 ​ sin α ​ = L ​ ​ l 1 ​ = 1 + s i n β s i n α ​ L ​ , l 2 ​ = sin β + sin α L sin β ​ × sin β sin α ​ ​ l 2 ​ = sin α + sin β L sin α ​ ​ m 1 ​ = sin α + sin β m sin β ​ , m 2 ​ = sin α + sin β m sin α ​ ​ Let α > β m 1 ​ g sin α − T = m 1 ​ a ​ a = m 1 ​ + m 2 ​ m 1 ​ g s i n α − m 2 ​ g s i n β ​ = 0 T − m 2 ​ g sin β = m 2 ​ a ​ ​

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