    Question

# Two semi-circular discs of mass density 1 kg/m2 and 2 kg/m2, radius r=1 m each are joined to form a complete disc. Find the moment of inertia (MI) of complete disc about an axis passing through it's centre.

A
π kg-m2
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B
2π kg-m2
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C
3π4 kg-m2
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D
π2 kg-m2
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Solution

## The correct option is C 3π4 kg-m2Let O be the centre of complete disc, axis of rotation is as shown in figure: Let the mass density of semi-circular discs be σ1 & σ2 σ1=1 kg/m2, σ2=2 kg/m2. ∵mass=σ×area Mass of the complete disk m=(m1+m2)=σ1(πR22)+σ2(πR22) m=1×(π(1)22)+2×(π×(1)22) ∴m=3π2 kg The MI of complete disc about an axis passing through it's centre and perpendicular to the plane: ⇒I=mr22 I=(3π2×122)=3π4 kg-m2 ∴I=3π4 kg-m2  Suggest Corrections  0      Similar questions  Related Videos   Moment of Inertia of Solid Bodies
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