A metal piece of mass 120 g is stretched to form a plane rectangular sheet of area of cross section `0.54m^(2)`. If length and breadth of this sheet are in the ratio 1:6, find its moment of inertia about an axis passing through its centre and perpendicular to its plane.

Explanation

Mass `M=120g=120xx10^(-3)kg`
area `lb=0.54m^(2)`
`(l)/(b)=(1)/(6)," ":.l=(b)/(6)`
`lb=0.54," "(b)/(6).b=0.54`
`b^(2)=0.54xx6impliesb=sqrt3.24=1.8m`
Similarly `l=(0.54)/(1.8)=0.3m`.
Moment of Inertia
`I=(M(l^(2)+b^(2)))/(12)=(120xx10^(-3)[(0.3)^(2)+(1.8)^(2)])/(12)`
`I=33.3xx10^(-3)kgm^(2)`