Question

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

• A. $\frac{I}{4}$
• B. $\frac{I}{2}$
• C. $2I$
• D. $4I$

Answer 1

Answer: (D)

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
$I^{\prime }=\frac{M{l}^2}{3}=4\left(\frac{M{l}^2}{12}\right)=4l$ (Using (i))