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JEE Main 2020 (9 Jan, Shift 1) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from JEE Main 2020 (9 Jan, Shift 1)

Q150JEE Main 2020 · 9 JAN · SHIFT 1Medium

Moment of Inertia & Radius of Gyration

Figure

Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres form an equilateral triangle of side of length d. The ratio I0/IA of moment of inertia I0 of the system about an axis passing through the centroid and about center of any of the spheres IA and perpendicular to the plane of the triangle is:

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Answer: (a)

  1. Each sphere: Icm=25m(d2)2=md210I_{cm} = \frac{2}{5}m\left(\frac{d}{2}\right)^2 = \frac{md^2}{10}; centroid to centre =d3= \frac{d}{\sqrt{3}}.
  2. I0=3(md210+md23)=13md210I_0 = 3\left(\frac{md^2}{10} + \frac{md^2}{3}\right) = \frac{13md^2}{10}
  3. IA=3×md210+2md2=23md210I_A = 3 \times \frac{md^2}{10} + 2md^2 = \frac{23md^2}{10}
  4. I0IA=1323\frac{I_0}{I_A} = \frac{13}{23}, so the answer is (a).
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