A metal piece of mass 120 g is stretched to form a plane rectangular sheet of area of cross section 0.54ms^(-1). 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.

A metal piece of mass 120 g is stretched to form a plane rectangular s

1.	A metal piece of mass 120 g is stretched to form a plane rectangular sheet of area of cross section 0.54ms^(-1). 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.
Answer» Solution :Mass M=120 g=`120xx10^(-3)kg`,area =lb=0.54 `m^(2)(L)/(b)=(1)/(6)` `therefore l=(b)/(6),ib0.54(b)/(6).b=0.545,b^(2)=0.54xx6impliesb=sqrt(3.24)1.8 m` SIMILARLY `l=(0.54)/(1.8)=0.3 m`. Moment of inertia `I(M(l^(2)+b^(2)))/(12)=(120xx10^(-3)(0.3)^(2)+(1.8)^(2))/(12)` =`(0.12xx(0.09+3.24))/(12)=(3.33)/(100)` `impliesI=33.3xx10^(-3)kg m^(2)`