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The moment of  inertia of a uniform semicircular wire of mass M and radius R about a line perpendicular to the plane of the wire through the centre is
9 months ago

Arun
24497 Points

The moment of inertia of a uniform semicircular wire of mass M and radius r about a line perpendicular to the plane of the wire through the center is
''Mr²''.

Explanation ⇒ According to the question, the mass of the wire is at a distance r away from the axis.
We know that the moment of the Inertia in such case will be given by the formula,
Moment of Inertia = Mv²
where, m is the mass and r is the Perpendicular distance.

9 months ago
Vikas TU
11138 Points

Dear student
Using Parallel Axis Theorem of MI
I1=I+mx^2
where I1= Moment of inertia about centre=mr^2
and I= Moment of inertia about centre of mass which is required
x=2r/π(distance between centre of mass of wire and its geometrical centre) THUS
I=I1−m(2r/π)^2
I=mr^2[1−4/π^2]
9 months ago
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### Course Features

• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions