Rotation Ques 33
- Seven identical circular planar discs, each of mass $M$ and radius $R$ are welded symmetrically as shown in the figure. The moment of inertia of the arrangement about an axis normal to the plane and passing through the point $P$ is
(2018 Main)
(a) $\frac{181}{2} M R^{2}$
(b) $\frac{19}{2} M R^{2}$
(c) $\frac{55}{2} M R^{2}$
(d) $\frac{73}{2} M R^{2}$
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Answer:
Correct Answer: 33.(a)
Solution:
Formula:
Two Important Theorems on Moment of Inertia :
- From the theorem of parallel axis,
$$ \begin{alignedat} & I=I_{cm}+ \frac{7}{5} M(3 R)^{2} \\ & =\frac{M R^{2}}{2}+6 \times \frac{M R^{2}}{2}+M(2 R)^{2} \quad+7 M(3 R)^{2}=\frac{181 M R^{2}}{2} \end{aligned} $$
BETA
