A system of a circular disc of mass $900 g$ and radius $4 m$ and a circular ring of mass $2 kg$ and radius $5 m$ are stacked about their common centre as shown in figure. What is the moment of inertia of the system about an axis passing through their common centre perpendicular to the plane of the disc and the ring?

65.4 {kgm}^{2}

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54.2 {kgm}^{2}

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50 {kgm}^{2}

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57.2 {kgm}^{2}

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Solution

The correct option is D $57.2 {kgm}^{2}$

Mass of disc $; M_{d} = 900 g = 0.9 kg$
Radius of disc $; R_{d} = 4 m$

Moment of inertia of disc
$I_{d} = \frac{M_{d} R_{d}^{2}}{2}$
$= \frac{0.9 \times 4^{2}}{2} = 7.2 {kg- m}^{2}$

Mas of ring $; M_{r} = 2 kg$
Radius of ring $; R_{r} = 5 m$

Moment of inertia of ring
$I_{r} = M_{r} R_{r}^{2}$
$= 2 \times 5^{2} = 50 {kg-m}^{2}$

Total moment of inerita of the system
$I_{n e t} = I_{r} + I_{d} = 50 + 7.2 = 57.2 {kg-m}^{2}$

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