This problem is reiated to Section $10\mathrm{.}8$ of the Textboak$]$

The assembly shown in the flisure below consists of a thin rod of lergth $l=23\mathrm{.}0cm$ and mass $m=1\mathrm{.}20kg$ with a solid ball of diameter $d=10\mathrm{.}0cm$ and mass $M=2\mathrm{.}00kg$ attached to its top. The assembly is free to pivat ahout a frictionless axie through the battam of the rod. The assembly is initially vertical and at rest when it starts to rotate clockwise.

Alter the combination rotates through $90$ degrees, what is its rotational binetic energy $($in J$)?$

$($A$)6\mathrm{.}84$ J

$($B$)5\mathrm{.}66$ J

$($C$)2\mathrm{.}58$ J

$($D$)7\mathrm{.}29$ J