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  4. The moment of inertia of a thin uniform rod of mass M and length l about an axis perpendicular to the rod through its centre is I . The moment of inertia of the rod through its end point is

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Q. The moment of inertia of a thin uniform rod of mass $M$ and length $l$ about an axis perpendicular to the rod through its centre is $I .$ The moment of inertia of the rod through its end point is

System of Particles and Rotational Motion

Solution:

The moment of inertia of a thin uniform rod of mass
$M$ and length $l$ about an axis perpendicular to the rod through
its centre is
$I=\frac{M l^{2}}{12} \,\,\,\,\,\, ....(i)$
The moment of inertia of the rod through its end point is
$I^{\prime}=\frac{M l^{2}}{3}=4\left(\frac{M l^{2}}{12}\right)=4 l$ $\,\,\,\,\,\,\,$ (Using (i))