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  4. From a triangular lamina of side a and mass m , a small triangular Lamina made by joining midpoints of sides of the triangular lamina is cut. The Moment of Inertia of complete Lamina about COM is Io . If the Moment of Inertia of remaining Lamina about the centroid is (p/q)I0 , then find the value of (p + q) . Where p and q are the least positive integers. <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-fnk231siwlsb.png />

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Q. From a triangular lamina of side a and mass $m$ , a small triangular Lamina made by joining midpoints of sides of the triangular lamina is cut. The Moment of Inertia of complete Lamina about COM is $I_{o}$ . If the Moment of Inertia of remaining Lamina about the centroid is $\frac{p}{q}I_{0}$ , then find the value of $\left(p + q\right)$ . Where $p$ and $q$ are the least positive integers.

Question

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

Dimension analysis
$I_{o}=KMa^{2}$
Now for small lamina
$I^{′}=K\frac{M}{4}\left(\frac{9}{2}\right)^{2}=\frac{k m a^{2}}{16}$
$I^{′}=\frac{I_{o}}{16}$
So moment of Inertia of remaining part
$I_{L}=I_{o}-I^{′}$
$=I_{o}-\frac{I_{o}}{16}$
$I_{L}=\frac{15 I_{o}}{16}$