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# A small spherical ball is released from a point at a height h on a rough track. Assuming that it does not slip any where , find its linear speed when it rolls on the horizontal part of the track.

$\begin {array} {1 1} (a)\;\sqrt {\frac{11\;gh}{7}} & \quad (b)\;\sqrt{\frac{3gh}{5}} \\ (c)\;\sqrt {\frac{7gh}{5}} & \quad (d)\;\sqrt {\frac{10gh}{7}} \end {array}$

$KE=PE$
$\large\frac{1}{2}mv^2 \bigg[ 1+ \large\frac{k^2}{r^2}\bigg]$$=mgh v^2 [1+ \large\frac{2}{3} \bigg]$$ =gh$
$=> v= \sqrt {\large\frac{3}{5} gh}$
edited Jun 24, 2014