Physics
Mechanics
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Question

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

  1. negative 2 fraction numerator G m over denominator l end fraction
  2. negative 3 square root of 2 fraction numerator G m over denominator l end fraction
  3. negative 2 square root of 2 fraction numerator G m over denominator l end fraction
  4. negative 4 square root of 2 fraction numerator G m over denominator l end fraction

The correct answer is: negative 4 square root of 2 fraction numerator G m over denominator l end fraction


    From figure,

    table attributes columnalign left end attributes row cell O A equals O B equals O C equals O D equals fraction numerator square root of l squared plus l squared end root over denominator 2 end fraction equals fraction numerator l square root of 2 over denominator 2 end fraction equals fraction numerator l over denominator square root of 2 end fraction end cell row cell V equals open parentheses fraction numerator G m over denominator O A end fraction close parentheses plus open parentheses negative fraction numerator G m over denominator O B end fraction close parentheses plus open parentheses negative fraction numerator G m over denominator O C end fraction close parentheses plus open parentheses negative fraction numerator G m over denominator O D end fraction close parentheses end cell row cell equals negative fraction numerator 4 G m over denominator l divided by square root of 2 end fraction equals negative 4 square root of 2 fraction numerator G m over denominator l end fraction end cell end table

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