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Question

A uniform chain of length 2m is held on a smooth horizontal table so that half of it hangs over the edge. If it is released from rest, the velocity with which it leaves the table will be nearest to 


  1. 2 m/s

  2. 4 m/s

  3. 6 m/s

  4. 8 m/s


Solution

The correct option is B

4 m/s


Taking surface of table as a reference level (zero potential energy)
Potential energy of chain when 1/nth length hanging from the edge
=MgL2n2
Potential energy of chain when it leaves the table =MgL2
Kinetic energy of chain = loss in potential energy
12Mv2=MgL2MgL2n212Mv2=MgL2[11n2]

Velocity of chain v=gL(11n2)=10×2(11(2)2)=15=3.87 4m/s(approx.)

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