Two uniform circular discs having the same mass and the same thickness, but different radii, are made from different materials. The disc with the smaller rotational inertia is:
A
the one made from the more dense material
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B
the one made from the less dense material
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C
the disc with the larger angular velocity
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D
the disc with the larger torque
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Solution
The correct option is A the one made from the more dense material
Given : M1=M2t1=t2
Let the densities of the two discs be ρ1 and ρ2 respectively.
Using M1=M2 we get ρ1×πR21t1=ρ2×πR22t2
⟹ρ1R21=ρ2R22 or, R21R22=ρ2ρ1 .............(1)
Moment of inertia of circular disc I=12MR2
⟹I1I2=R21R22=ρ2ρ1
Thus if ρ1>ρ2⟹I1<I2
Hence the disc made up of more dense material has smaller rotational inertia.