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JEE Main 2026 (24 Jan, Shift 2) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from JEE Main 2026 (24 Jan, Shift 2)

Q38JEE Main 2026 · 24 JAN · SHIFT 2Difficult

Moment of Inertia & Radius of Gyration

A uniform solid cylinder of length LL and radius RR has moment of inertia about its axis equal to I1I_1. A small co-centric cylinder of length L/2L/2 and radius R/3R/3 carved from this cylinder has moment of inertia about its axis equals to I2I_2. The ratio I1/I2I_1/I_2 is ______.

Numerical answer type. Work it out, then open the answer.

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Answer: 162

  1. I1=MR22I_1 = \frac{MR^2}{2}
  2. Carved mass =M×19×12=M18= M \times \frac{1}{9} \times \frac{1}{2} = \frac{M}{18}: I2=12M18R29I_2 = \frac{1}{2}\frac{M}{18}\frac{R^2}{9}
  3. I1I2=18×9=162\frac{I_1}{I_2} = 18 \times 9 = 162
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