MCQ
In a rectangle $ABCD\,\,(BC = 2AB)$. The moment of inertia along which axis will be minimum
- A$BC$
- B$BD$
- C$HF$
- ✓$EG$
✓
Answer
Correct option: D.
$EG$
d
The moment of inertia will be minimum about that axis, which is passing through the center of mass.
The moment of inertia will be minimum about that axis, which is passing through the center of mass.
$I_{E G}=\frac{M B^{2}}{12}$
$I_{F H}=\frac{M(2 B)^{2}}{12}=\frac{M B^{2}}{6}$
$M. I.$ of the rectangular plate about its diagonal $I_{B D}=\frac{M B^{2} L^{2}}{6\left(B^{2}+L^{2}\right)}=\frac{M B^{2} \times 4 B^{2}}{6\left(B^{2}+4 B^{2}\right)}=\frac{2}{15} M B^{2}=\frac{M B^{2}}{7.5}$
$M. I.$ about $E G$ is minimum.
$\mathrm{OR}$
By observation, distribution of mass is the nearest about axis $E G .$
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