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. $2\,ma^2$
• B. $4\,ma^2$
• C. $2\,m(a^2 + b^2)$
• D. $2\,m(a^2 - b^2)$

Answer 1

Answer: (A)

The given situation can be shown as

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