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A chain (AB) of length l loaded in a smo...

A chain (AB) of length `l` loaded in a smooth horizontal table so that its fraction of length h hangs freely and toucher the surface of the table with its end B. At a certain moment ,the end A of the chain is set free. With what velocity will this end the chain slip out of the table ?
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Text Solution

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The correct Answer is:
B
At the instant show in figure, net pulling force
`=m/lgh`

Total mass being pulled `=m/l(x+h)`
`:.` Acceleration `a=("Net pulling force")/("Total mass being pulled")`
`=(gh)/(x+h)`
`:. V(-(dv)/(dx))=(gh)/(x+h)`
or `int_(0)^(v)v.dv=-gh int_(l-h)^(0)(dx)/(x+h)`
or `v^(2)/2 =gh` ln `(l/h)`
`v=sqrt(2ghIn(l//h))`.
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