Physics
Mechanics
Easy

Question

A body hanging from a spring stretches it by 1 cm at the earth's surface. How much will the same body stretch the spring at a place 16400 km above the earth's surface? (Radius of the earth =6400 km)

  1. 1.28 cm
  2.  0.64 cm
  3. 3.6 cm
  4. 0.12 cm

The correct answer is: 0.64 cm


    At the earth's surface, m g equals k cross times x
    At a height h comma m g to the power of apostrophe equals k cross times x
    table attributes columnalign left end attributes row cell g to the power of apostrophe over g equals x to the power of apostrophe over x equals fraction numerator R subscript e superscript 2 over denominator open parentheses R subscript e plus h close parentheses squared end fraction equals fraction numerator left parenthesis 6400 right parenthesis squared over denominator left parenthesis 6400 plus 1600 right parenthesis squared end fraction end cell row cell equals open parentheses 6400 over 8000 close parentheses squared equals 16 over 25 end cell row cell x to the power of apostrophe equals 16 over 25 cross times x equals 16 over 25 cross times 1 c m equals 0.64 c m end cell end table

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