$3)$ LABORATORY QUESTION

A setup to determine the moment of inertia using energy conservation includes a pulley with a radius $\backslash ($ r$=2\backslash$mathrm$\{$~cm$\}\backslash )$ attached under a reference table. A string is wound around the pulley, with a mass of $10$ g attached to the string's end. The string passes over an massless and frictionless pulley and hangs vertically with mass $\backslash ($ m $\backslash ).$ When the system is released, the time it takes for $\backslash ($ m $\backslash )$ to fall a vertical distance $\backslash ($ h$=100\backslash$mathrm$\{$~cm$\}\backslash )$ is measured, and the reference table's moment of inertia is determined to be $\backslash (760\backslash$mathrm$\{$~g$\}\backslash$mathrm$\{$~cm$\}^\{2\}\backslash ).$ When a homogeneous equilateral triangular plate is placed on the reference table with its center of mass aligned with the rotation axis, it is found that $\backslash ($ m $\backslash )$ takes $5$ s to travel the same distance. What is the moment of inertia of the equilateral triangular plate relative to its center of mass in $\backslash (\backslash$mathrm$\{$cm$\}^\{2\}\backslash )?($All frictional forces are neglected$)$

A$)4200$

B$)1200$

C$)3200$

D$)5200$

E$)2200$