PhysicsA uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be

A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be

  1. A

    2a3, 2b3

  2. B

    5a12, 5b12

  3. C

    3a4, 3b4

  4. D

    5a3, 5b3

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    Solution:

    solution

    Here, Area of a full lamina, A1=ab

    Area of the lamina's darkened portion = a2×b2=ab4

    Using centre of mass,

    xcm=A1x1-A2x2A1-A2

    xcm=aba2-ab43a4ab-ab4

    xcm=8a2b-3a2b163ab4=5a12

    ycm=A1y1-A2y2A1-A2

    ycm=abb2-ab43b4ab-ab4=5b12

    Hence the correct answer is 5a12,5b12.

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