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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 - Physics

MCQ
Fill in the Blanks

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 ___________ .

Options

  • \[M r^2\]

  • \[\frac{1}{2}M r^2\]

  • \[\frac{1}{4}M r^2\]

  • \[\frac{2}{5}M r^2\]

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Solution

\[M r^2\]

 

Consider an element of length, dl = rdθ.

\[dm = \frac{M}{\pi r}dl = \frac{M}{\pi r}rd\theta\]

MOI of semicircular wire = \[\int_0^\pi  r^2 dm\]

\[I =  \int_0^\pi  r^2 \frac{m}{\pi r}rd\theta\] 

\[ \Rightarrow I = m r^2\]

  Is there an error in this question or solution?
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APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 10 Rotational Mechanics
MCQ | Q 14 | Page 193
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