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JEE Main 202118 MarchEvening Shift
Exam
JEE Main
Year
2021
Date
18 March
Shift
Evening Shift
Subject
Physics
Chapter
Rotational Motion

JEE Main 2021 · 18 March · Evening Shift · Physics · Rotational Motion

Consider a uniform wire of mass M and length L . It is bent into a...

Consider a uniform wire of mass MM and length LL. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is :

Options

  1. A14ML2π2\dfrac{1}{4}\dfrac{M{L}^{2}}{{\pi}^{2}}
  2. B25ML2π2\dfrac{2}{5}\dfrac{M{L}^{2}}{{\pi}^{2}}
  3. CML2π2\dfrac{M{L}^{2}}{{\pi}^{2}}
  4. D12ML2π2\dfrac{1}{2}\dfrac{M{L}^{2}}{{\pi}^{2}}

Correct answer

C. ML2π2\dfrac{M{L}^{2}}{{\pi}^{2}}

Step-by-step solution

\pir=L⇒r=Lπ\pir = L ⇒ r = \dfrac{L}{\pi}
I=Mr2=ML2π2I = M{r}^{2} = \dfrac{M{L}^{2}}{{\pi}^{2}}
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