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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

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

Grade:12th pass

2 Answers

Arun
25750 Points
4 years ago
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. 

 
 
Vikas TU
14149 Points
4 years ago
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]

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