Physics
Mechanics
Easy

Question

If both the mass and radius of the earth decrease by 1%, the value of

  1. acceleration due to gravity would decrease by nearly 1%
  2. acceleration due to gravity would increase by 1%
  3. escape velocity from the earth's surface would decrease by 1%
  4. the gravitational potential energy of a body on earth's surface will remain unchanged

The correct answers are: acceleration due to gravity would increase by 1%, the gravitational potential energy of a body on earth's surface will remain unchanged


    The acceleration due to gravity is .g equals fraction numerator G M over denominator R squared end fraction
    The new value of g would be  g to the power of apostrophe equals fraction numerator G left parenthesis 0.99 M right parenthesis over denominator left parenthesis 0.99 R right parenthesis squared end fraction equals 1.01 fraction numerator G M over denominator R squared end fraction
    Thus, g would increase by about 1%. The new escape velocity would be
    v to the power of apostrophe equals square root of fraction numerator 2 cross times 0.99 M cross times G over denominator 0.99 R end fraction end root equals square root of fraction numerator 2 M G over denominator R end fraction end root equals v subscript e
minus fraction numerator G m left parenthesis 0.99 M right parenthesis over denominator left parenthesis 0.99 R right parenthesis end fraction equals negative fraction numerator G m M over denominator R end fraction

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