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NEET2026PhysicsChapterActual

A uniform thin wire of length l and linear mass density is bent to form a closed circular loop. The loop is placed in a horizontal plane. What is the moment of inertia of this loop about a vertical axis passing through a point on its circumference, as shown in the figure?

Options

  1. Al^3 4 ^2
  2. Bl^3 2 ^2
  3. C3 l^3 8 ^2
  4. Dl^2 2 ^2

Correct answer

B. l^3 2 ^2

Step-by-step solution

Total mass of the loop, M = l Let R be the radius of the circular loop. The circumference is equal to the length of the wire: 2 R = l R = l 2 The moment of inertia of the circular loop about an axis passing through its center and perpendicular to its plane is: I_C = M R^2 The required axis Z-Z' passes through a point on the circumference and is parallel to the central axis. Using the parallel axis theorem, the moment of inertia about this axis is: I = I_C + M R^2 = M R^2 + M R^2 = 2 M R^2 Substituting the values of

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