NEET-XII-Physics
10: Rotational Mechanics
- #14The 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
(a)
Mr2
(b)
12Mr2
(c)
14Mr2
(d)
25Mr2.digAnsr: aAns : (a) `` M{r}^{2}``
Consider an element of length, dl = rdθ.
`` dm=\frac{M}{\,\mathrm{\,\pi \,}r}dl=\frac{M}{\,\mathrm{\,\pi \,}r}rd\theta ``
MOI of semicircular wire = `` {\int }_{0}^{\,\mathrm{\,\pi \,}}{r}^{2}dm``
`` I={\int }_{0}^{\,\mathrm{\,\pi \,}}{r}^{2}\frac{m}{\,\mathrm{\,\pi \,}r}rd\theta ``
`` \Rightarrow I=m{r}^{2}``
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