A hollow cylinder has mass M. outside radius $R_{2}$ and inside radius $R_{1}$ Its moment of inertia about an or axis parallel to its symmetry axis and tangential to tho outer surface is equal to :

\frac{M}{2} (R_{2}^{2} + R_{1}^{2})

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\frac{M}{2} (R^{2} - R_{1}^{2})

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\frac{M}{4} {(R_{2} + R_{1})}_{2}^{2}

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\frac{M}{2} (3 R_{2}^{2} + R_{1}^{2})

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Solution

The correct option is C $\frac{M}{2} (3 R_{2}^{2} + R_{1}^{2})$
REF.Image
According to the quation we have t find the moment of inertia about XX' axis.
MOI of figure about symmetric axis i.e., axis passing through COM
$(I_{C M})_{w h o l e} = (I_{C M})_{R_{2}} + (I_{C M}) R_{1}$
$= \frac{M R_{2}^{2}}{2} + \frac{M R_{1}^{2}}{2}$
$= \frac{M}{2} (R_{2}^{2} + R_{1}^{2})$
Then, by parallel axis theorem
$I_{X X^{'}} = (I_{c m})_{w h o l e} + M R_{2}^{2}$
$= \frac{M}{2} (R_{2}^{2} + R_{1}^{2}) + \frac{2}{2} M R_{2}^{2}$
$I_{X X^{'}} = \frac{M}{2} (3 R_{2}^{2} + R_{1}^{2})$

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A hollow cylinder has mass M. outside radius R2 and inside radius R1 Its moment of inertia about an or axis parallel to its symmetry axis and tangential to tho outer surface is equal to :

A hollow cylinder has mass M. outside radius $R_{2}$ and inside radius $R_{1}$ Its moment of inertia about an or axis parallel to its symmetry axis and tangential to tho outer surface is equal to :