Mass of the disc in terms of density can be written as, m=ρ(πR2t).
⇒R2=ρπtm
Now moment of inertia of the disc about the diameter is, 4mR2.
Therefore,
I=4mR2=4ρπtm2⇒I∝ρt1
Required ratio, I2I1=ρ1t1ρ2t2=35×10.5=65
Hence, x=5.
Two discs of same mass and different radii are made of different materials such that their thicknesses are 1cm and 0.5cm respectively. The densities of materials are in the ratio 3:5. The moment of inertia of these discs respectively about their diameters will be in the ratio of 6x. The value of x is ______.
Held on 31 Jan 2023 · Verified 6 Jul 2026.
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