Question

Four small objects each of mass m are fixed at the corners of a rectangular wire-frame of negligible mass and of sides $a$ and $b(a>b)$. If the wire frame is now rotated about an axis passing along the side of length b, then the moment of inertia of the system for this axis of rotation is

• A. $2m{a}^2$
• B. $4m{a}^2$
• C. $2m(a^2+b^2)$
• D. $2m(a^2-b^2)$

Answer 1

Answer: (A)

The given situation can be shown as

Moment of inertia of the system about side of length $b$ say $CD$ is
$=$ M.I. of mass at $A$ about $CD+M.I.$ of mass at $B$ about $CD+M.I$. of mass at $C$ about $CD$ $+$ M.I. of mass ot $D$ about $CD$
$=m(a{)}^2+m(a{)}^2+m(0{)}^2+m(0{)}^2$
$=2m{a}^2$