physics
mechanics
Easy

Question

Four particles each of mass m are placed at the vertices of a square of side . The potential energy of the system is

  1. negative fraction numerator 2 G m squared over denominator l end fraction open parentheses 2 plus fraction numerator 1 over denominator square root of 2 end fraction close parentheses
  2. negative fraction numerator square root of 2 G m squared over denominator l end fraction open parentheses 2 minus fraction numerator 1 over denominator square root of 2 end fraction close parentheses
  3. negative fraction numerator 2 G m squared over denominator l end fraction open parentheses square root of 2 minus fraction numerator 1 over denominator square root of 2 end fraction close parentheses
  4. negative fraction numerator 2 G m squared over denominator l end fraction open parentheses square root of 2 plus fraction numerator 1 over denominator square root of 2 end fraction close parentheses

The correct answer is: negative fraction numerator 2 G m squared over denominator l end fraction open parentheses 2 plus fraction numerator 1 over denominator square root of 2 end fraction close parentheses


    From figure

    table attributes columnalign left end attributes row cell text  A  end text B equals B C equals C D equals A D equals 1 end cell row cell therefore A C equals B D equals square root of l squared plus l squared end root equals l square root of 2 end cell row cell U equals open parentheses negative fraction numerator G cross times m cross times m over denominator A B end fraction close parentheses plus open parentheses negative fraction numerator G cross times m cross times m over denominator A C end fraction close parentheses plus open parentheses negative fraction numerator G cross times m cross times m over denominator A D end fraction close parentheses plus open parentheses negative fraction numerator G cross times m cross times m over denominator B C end fraction close parentheses end cell row cell    plus open parentheses negative fraction numerator G cross times m cross times m over denominator B D end fraction close parentheses plus open parentheses negative fraction numerator G cross times m cross times m over denominator C D end fraction close parentheses end cell row cell equals negative fraction numerator 4 G m squared over denominator l end fraction minus fraction numerator 2 G m squared over denominator l square root of 2 end fraction equals negative fraction numerator 2 G m squared over denominator l end fraction open parentheses 2 plus fraction numerator 1 over denominator square root of 2 end fraction close parentheses end cell end table

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