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JEE Main 202116 MarchMorning Shift
Exam
JEE Main
Year
2021
Date
16 March
Shift
Morning Shift
Subject
Physics
Chapter
Rotational Motion

JEE Main 2021 · 16 March · Morning Shift · Physics · Rotational Motion

Four equal masses, m each are placed at the corners of a square of...

Four equal masses, mm each are placed at the corners of a square of length (l)\left(l\right) as shown in the figure. The moment of inertia of the system about an axis passing through AA and parallel to DBDB would be :

Four equal masses, m each are placed at the corners of a square of length (l) as shown in the figure. The moment of

Options

  1. Aml2m{l}^{2}
  2. B2ml22m{l}^{2}
  3. C3ml23m{l}^{2}
  4. D3ml2\sqrt{3}m{l}^{2}

Correct answer

C. 3ml23m{l}^{2}

Step-by-step solution

Moment of inertia of point mass = mass ×\times (Perpendiculardistancefromaxis)2{\left(Perpendiculardistancefromaxis\right)}^{2}

Four equal masses, m each are placed at the corners of a square of length (l) as shown in the figure. The moment of

Moment of Inertia

=m(0)2+m(l2)2+m(l2)2+m(l2)2= m{\left(0\right)}^{2} + m{\left(l\sqrt{2}\right)}^{2} + m{\left(\dfrac{l}{\sqrt{2}}\right)}^{2} + m{\left(\dfrac{l}{\sqrt{2}}\right)}^{2}

=3ml2= 3m{l}^{2}

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