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 ''. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cro

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Solution

Q.
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 ' $α$ '. 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: [2025]

1 $α$

2 $α / 4$

3 $α / 8$

4 $α / 2$

Ans.
(2)

Moment of inertia of the rod in $I^{st}$ case,

$α = \frac{M l^{2}}{12}$

Moment of inertia of the rod in ${II}^{nd}$ case,

$α' = 2 [\frac{\frac{M}{2} {(\frac{l}{2})}^{2}}{12}] = \frac{M l^{2}}{48} = \frac{α}{4}$

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