Question

Ametal piece of mass 120g is stretched to form a plane, rectangular sheet of area cross section 0.54m². if the length and breadth of this sheet are in the ratio1:6. find its moment of inertia about an axis passing through its centre and perpendicular to plane.

Answer 1

$$\begin{gathered} \mathrm{Suppose}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{sheet}=\text{'}\mathrm{l}\text{'}\mathrm{m} \\ \mathrm{Then},\mathrm{according}\mathrm{to}\mathrm{question}, \\ \mathrm{Breadth}\mathrm{of}\mathrm{sheet},\mathrm{b}=\text{'}6\mathrm{l}\text{'}\mathrm{m} \\ \mathrm{Area}=\mathrm{l}\times \mathrm{b}=\mathrm{l}\times 6\mathrm{l}=6{\mathrm{l}}^2=0.54{\mathrm{m}}^2 \\ \mathrm{or}\mathrm{l}=0.3\mathrm{m} \\ \mathrm{and}\mathrm{b}=1.8\mathrm{m} \\ \mathrm{Now}, \\ \mathrm{Mass}\mathrm{of}\mathrm{the}\mathrm{sheet},\mathrm{M}=120\mathrm{g}=0.12\mathrm{kg} \\ \mathrm{Moment}\mathrm{of}\mathrm{inertia}\mathrm{is}\mathrm{given}\mathrm{by}, \\ \mathrm{I}=\frac{\mathrm{M}({\mathrm{l}}^2+{\mathrm{b}}^2)}{12} \\ =\frac{0.12(0.3^2+1.8^2)}{12} \\ =3.33\times {10}^{-2}\mathrm{kg}-{\mathrm{m}}^3 \end{gathered}$$