A heavy, flexible, uniform chain of length 
and mass 
lies in a smooth semi-circular tube AB of radius r. Assuming a slight disturbance to start the chain in motion, if velocity v with which it will emerge from the end B of the tube is 
, then x is
Text Solution
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(2)
Since friction is absent, we can apply the law of conservation of energy. Centre of gravity of a semicircular arc is at a distance ( 
) from centre.
When the chain is completely slipped off the tube, all the links of the chain have the same velocity u.
Kinetic energy of chain 
From COE,
From which we find
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