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.
JEE Main 2023 — Physics Mechanics
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