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

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 0.54 m^(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.
Answer» Solution :Mass M = 120 g = `120xx10^(-3)kg` area `= lb =0.54 m^(2)` `(L)/(b)=(1)/(6), "" therefore l=(b)/(6)` `lb=0.54 , "" (b)/(6).b=0.54` `b^(2)=0.54xx6 rArr b = sqrt(3.24)=1.8 m`. SIMILARLY `l = (0.54)/(18)=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)kg m^(2)`.