How to fing the acceleration of one body hanged from pulley
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★ Let's take origin at top pulley which is at rest.
Note that length of top rope is constant : a+b=k⟹a′′+b''=0⟹a′′=−b′′a+b=k⟹a″+b″=0⟹a″=−b″
Also Length of second rope is constant : (c−b)+(d−b)=k⟹c′′+d′′=2b′′(c−b)+(d−b)=k⟹c″+d″=2b″
Note that dd is a constant as the top pulley and ground is rest : c′′=2b′′c″=2b″
Hence, c′′=−2a′′c″=−2a″ as stated in comments.
Also, everything we have done is futile and the block M2M2 will hit the ground very quickly.
Note that length of top rope is constant : a+b=k⟹a′′+b''=0⟹a′′=−b′′a+b=k⟹a″+b″=0⟹a″=−b″
Also Length of second rope is constant : (c−b)+(d−b)=k⟹c′′+d′′=2b′′(c−b)+(d−b)=k⟹c″+d″=2b″
Note that dd is a constant as the top pulley and ground is rest : c′′=2b′′c″=2b″
Hence, c′′=−2a′′c″=−2a″ as stated in comments.
Also, everything we have done is futile and the block M2M2 will hit the ground very quickly.
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