Physics-
General
Easy

Question

The distance of the centre of mass of the T-shaped plate from O is

  1. 7 m    
  2. 2.7 m    
  3. 4 m    
  4. 1 m    

The correct answer is: 2.7 m


    Co-ordinate of CM is given by
    X subscript C M end subscript equals fraction numerator m subscript 1 end subscript x subscript 1 end subscript plus m subscript 2 end subscript x subscript 2 end subscript over denominator m subscript 1 end subscript plus m subscript 2 end subscript end fraction

    Taking parts A and B as two bodies of same system
    m subscript 1 end subscript equals l cross times b cross times sigma equals 8 cross times 2 cross times sigma equals 16 sigma
    m subscript 2 end subscript equals l cross times b cross times sigma equals 6 cross times 2 cross times sigma equals 12 sigma
    Choosing O as origin,
    x subscript 1 end subscript equals 1 blank m comma blank x subscript 2 end subscript equals 2 plus 3 equals 5 blank m
    therefore X subscript C M end subscript equals fraction numerator 16 sigma cross times 1 plus 12 sigma cross times 5 over denominator 16 sigma plus 12 sigma end fraction equals fraction numerator 19 over denominator 7 end fraction
    equals 2.7 blank m f r o m O

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