Physics-
General
Easy

Question

Three rods of the same mass are placed as shown in figure. What will be the coordinates of centre of mass of the system?

  1. open square brackets fraction numerator a over denominator 2 end fraction comma fraction numerator a over denominator 2 end fraction close square brackets    
  2. open square brackets fraction numerator a over denominator square root of 2 end fraction comma fraction numerator a over denominator square root of 2 end fraction close square brackets    
  3. [square root of 2 a comma square root of 2 a]    
  4. open square brackets fraction numerator a over denominator 3 end fraction comma fraction numerator a over denominator 3 end fraction close square brackets    

The correct answer is: open square brackets fraction numerator a over denominator 3 end fraction comma fraction numerator a over denominator 3 end fraction close square brackets


    As shown in figure, centre of mass of respective rods are at their respective mid points. Hence centre of mass of the system has coordinates (X subscript C M end subscript,Y subscript C M end subscript). then

    X subscript C M end subscript equals fraction numerator m cross times fraction numerator a over denominator 2 end fraction plus m cross times fraction numerator a over denominator 2 end fraction plus m cross times 0 over denominator 3 m end fraction equals fraction numerator a over denominator 3 end fraction
    Y subscript C M end subscript equals fraction numerator m cross times 0 plus m cross times fraction numerator a over denominator 2 end fraction plus m cross times 0 over denominator 3 m end fraction equals fraction numerator a over denominator 3 end fraction

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