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Question

The change in potential energy when a body of mass m is raised to a height n RE from earth's surface is (RE. radius of the earth)

  1. m g R subscript E fraction numerator n over denominator left parenthesis n minus 1 right parenthesis end fraction
  2. m g R subscript E
  3. m g R subscript capital sigma fraction numerator n over denominator left parenthesis n plus 1 right parenthesis end fraction
  4. fraction numerator m g R subscript g with bar below end subscript over denominator n end fraction

The correct answer is: m g R subscript capital sigma fraction numerator n over denominator left parenthesis n plus 1 right parenthesis end fraction


    U equals negative fraction numerator G m subscript capital sigma m over denominator r end fraction
    At the surface of the earth, r equals R subscript E
    table attributes columnalign left end attributes row cell U subscript 1 equals negative fraction numerator G M subscript E m over denominator R subscript E end fraction end cell row cell r equals R subscript E plus h equals R subscript E plus n R subscript E equals left parenthesis 1 plus n right parenthesis R subscript E end cell row cell therefore U subscript 2 equals negative fraction numerator G M subscript E m over denominator left parenthesis n plus 1 right parenthesis R subscript E end fraction end cell row cell capital delta U equals U subscript 2 minus U subscript 1 equals negative fraction numerator G M subscript E m over denominator left parenthesis n plus 1 right parenthesis R subscript E end fraction minus open parentheses negative fraction numerator G M subscript E m over denominator R subscript E end fraction close parentheses end cell row cell equals fraction numerator G M subscript E m over denominator R subscript E end fraction open parentheses 1 minus fraction numerator 1 over denominator left parenthesis n plus 1 right parenthesis end fraction close parentheses equals fraction numerator G M subscript E m m over denominator left parenthesis n plus 1 right parenthesis R subscript E end fraction end cell row cell equals m g R subscript E fraction numerator n over denominator left parenthesis n plus 1 right parenthesis end fraction    open parentheses because g equals fraction numerator G M subscript E over denominator R subscript E superscript 2 end fraction close parentheses end cell end table

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