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Question

Moment of inertia of uniform triangular plate about axis passing through sides AB,AC, BC are IP,IB and IH respectively and about an axis perpendicular to the plane and passing through point C is IC, then :

  1. I subscript C greater than I subscript P greater than I subscript B greater than I subscript H
  2. I subscript H greater than I subscript B greater than I subscript C greater than I subscript P
  3. I subscript p greater than I subscript I l end subscript greater than I subscript B greater than I subscript C
  4. none of these

The correct answer is: I subscript C greater than I subscript P greater than I subscript B greater than I subscript H


    Moment of inertia is more when mass is farther from the axis. In case of axis BC, mass distribution is closest to it and in case of axis AB mass distribution is farthest. Hence

    I subscript B C end subscript less than I subscript A C end subscript less than I subscript A B end subscript not stretchy rightwards double arrow I subscript P greater than I subscript B greater than I subscript H
    I subscript C equals I subscript C M end subscript plus m y squared equals I subscript B superscript apostrophe minus m x squared plus m y squared
    Here I subscript B superscript apostrophe is moment of inertia of the plate about an axis perpendicular to it and passing through B.
    not stretchy rightwards double arrow space of 1em I subscript C equals I subscript B superscript straight prime plus m left parenthesis y squared minus x squared right parenthesis equals I subscript P plus I subscript B plus m left parenthesis y squared minus x squared right parenthesis
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row blank cell text It means  end text I subscript C greater than I subscript P plus I subscript B space space text also   end text I subscript C greater than I subscript P end cell row blank cell therefore space of 1em I subscript C greater than I subscript P greater than I subscript B greater than I subscript H end cell end table

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