Moment of inertia of a rod of mass ' M ' and length 'L' about an … - Vidyadip

MCQ

Moment of inertia of a rod of mass ' M ' and length 'L' about an axis passing through its center and normal to its length is ' $\alpha$ '. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to plane containing cross is :

A
$\alpha$
✓
$\alpha / 4$
C
$\alpha / 8$
D
$\alpha / 2$

✓

Answer

Correct option: B.

$\alpha / 4$

(B) $\alpha / 4$
Explanation:

$\alpha=\frac{M \ell^2}{12}$ ....(i)

$\alpha^{\prime}=2\left[\frac{\frac{ M }{2}\left(\frac{\ell}{2}\right)^2}{12}\right]$
$\alpha^{\prime}=\frac{ M \ell^2}{48}=\frac{\alpha}{4}$
Correct option is (B)

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