Velocity of Chain While Leaving the Table
Category : JEE Main & Advanced
Taking surface of table as a reference level (zero potential energy)
Potential energy of chain when 1/nth length hanging from the edge \[=\frac{-MgL}{2{{n}^{2}}}\]
Potential energy of chain when it leaves the table \[=-\frac{MgL}{2}\]
Kinetic energy of chain = loss in potential energy
\[\Rightarrow \] \[\frac{1}{2}M{{v}^{2}}=\frac{MgL}{2}-\frac{MgL}{2{{n}^{2}}}\]
\[\Rightarrow \] \[\frac{1}{2}M{{v}^{2}}=\frac{MgL}{2}\left[ 1-\frac{1}{{{n}^{2}}} \right]\]
\[\therefore \] Velocity of chain \[v=\sqrt{gL\left( 1-\frac{1}{{{n}^{2}}} \right)}\]
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