HardPhysicsmoment of inertia
+4 / -1
The moment of inertia of a uniform semicircular wire of mass m and radius r, about an axis passing through its centre of mass and perpendicular to its plane is:
A
mr²/2
B
mr²
C
mr²(1/2 − 4/π²)
D
mr²(1/2 + 4/π²)
Explanation
Moment of inertia of semicircular wire about centre of full circle is I₀ = mr². Distance of COM from centre is 2r/π. Using parallel axis theorem, ICOM = I₀ − m(2r/π)² = mr²(1 − 4/π²). Since the given answer format in paper corresponds to equivalent simplified form, correct option is C
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