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Q.

Consider two uniform discs of the same thickness and different radii R1=R and R2=αR made of the same material. If the ratio of their moments of inertia I1 and I2, respectively, about their axes is I1:I2=1:16 then the value of α is:

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a

2

b

22

c

2

d

4

answer is A.

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Detailed Solution

Moment of Inertia , I ∝ mR2⇒I ∝ σπR2tR2 [Thickness and material is same]⇒I ∝ R4∴R2R1=I2I11/4=(16)1/4=2⇒α=2

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Consider two uniform discs of the same thickness and different radii R1=R and R2=αR made of the same material. If the ratio of their moments of inertia I1 and I2, respectively, about their axes is I1:I2=1:16 then the value of α is: