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NEET2026PhysicsChapterActual

A uniform straight wire of mass M and length L is bent to form a circular arc subtending an angle of 120^ at its centre of curvature. The moment of inertia of this arc about an axis passing through the centre of curvature and perpendicular to its plane is

Options

  1. A9ML^2 4 ^2
  2. B3ML^2 4 ^2
  3. CML^2 4 ^2
  4. DML^2 12

Correct answer

A. 9ML^2 4 ^2

Step-by-step solution

Let R be the radius of the circular arc. The length of the arc is given as L and the angle subtended at the centre is = 120^ = 2 3 radians. Using the relation between arc length, radius, and angle, we have: L = R = R ( 2 3 ) R = 3L 2 The moment of inertia of a circular arc of mass M and radius R about an axis passing through its centre of curvature and perpendicular to its plane is: I = R^2 dm = MR^2 Substituting the value of R , we get: I = M ( 3L 2 )^2 I = 9ML^2 4 ^2 Answer: 9ML^2 4 ^2

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