$1.$ A long link chain of linear density $\backslash (\backslash$rho$=2\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}\backslash )$ supports a block of mass $\backslash ($ M$=20\backslash$mathrm$\{$~kg$\}\backslash )$ at $\backslash ($ h$=3\backslash$mathrm$\{$~m$\}\backslash )$ from the ground using an ideal ceiling$-$fixed pulley in a uniform gravitational field with $\backslash ($ g$=10\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash ),$ as shown. If the chain is suddenly released from rest, determine $($a$)$ the velocity of the block when it hits the ground, and $($b$)$ the velocity of the chain as a function of time after the block hits the ground and stops. Assume that the height of the chain heap is negligible such that length of the chain on both sides of the pulley is $5$ m after the block hits the ground, and ignore the small amount of chain on the pulley.

$\backslash [$

$(9+5)$

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