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Mechanics
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Question

The intensity of gravitational field at a point situated at a distance of 8000 km from the centre of the earth is 6 N / kg. The gravitational potential at that point is - (in Joule/ kg)

  1. 8 cross times 10 to the power of 6
  2. 2.4 cross times 10 cubed
  3. 4.8 cross times 10 to the power of 7
  4. 6.4 cross times 10 to the power of 14

The correct answer is: 2.4 cross times 10 cubed


    When body starts falling toward earth's surface its potential energy decreases so kinetic energy increases.
    Increase in kinetic energy = Decrease in potential energy
    Final kinetic energy - Initial kinetic energy = Initial potential energy - Final potential energy
    Final kinetic energy – 0
    equals open parentheses negative fraction numerator G M n over denominator r subscript 1 end fraction close parentheses minus open parentheses negative fraction numerator G M m over denominator r subscript 2 end fraction close parentheses
    therefore Final kinetic energy equals open parentheses fraction numerator negative G M m over denominator R plus h subscript 1 end fraction close parentheses minus open parentheses negative fraction numerator G M m over denominator R plus h subscript 2 end fraction close parentheses
    table attributes columnalign left end attributes row cell equals open parentheses negative fraction numerator G M m over denominator R plus 2 R end fraction close parentheses minus open parentheses negative fraction numerator G M m over denominator R plus R end fraction close parentheses end cell row cell equals negative fraction numerator G M m over denominator 3 R end fraction plus fraction numerator G M m over denominator 2 R end fraction equals 1 over 6 fraction numerator G M m over denominator R end fraction end cell end table

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