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JEE Main 2023 (13 Apr, Shift 1) · Rolling Motion

Rolling Motion question from JEE Main 2023 (13 Apr, Shift 1)

Q46JEE Main 2023 · 13 APR · SHIFT 1Difficult

Rolling Motion

A disc is rolling without slipping on a surface. The radius of the disc is RR. At t=0t = 0, the top most point on the disc is AA as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is

Figure

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Answer: (c)

  1. In half a rotation the centre moves πR\pi R forward (rolling without slipping).
  2. Point A goes from the top to the bottom: horizontal shift πR\pi R, vertical drop 2R2R.
  3. Displacement =(πR)2+(2R)2=Rπ2+4= \sqrt{(\pi R)^2 + (2R)^2} = R\sqrt{\pi^2 + 4}.
  4. So the answer is (c).
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