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Motion In Straight Line

Question
CBSEENPH11020594

A spherical planet has a mass Mp and diameter Dp. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to

  • 4GMp/Dp2

  • GMpm/Dp2

  • GMpm/ Dp2

  • 4GMpm/Dp2

Solution

A.

4GMp/Dp2

Force comma
straight F equals space fraction numerator GM subscript straight e straight m over denominator straight R squared end fraction
Here comma space
straight F space equals fraction numerator GM subscript straight p straight m over denominator left parenthesis straight D subscript straight p divided by 2 right parenthesis squared end fraction
straight F space equals space fraction numerator 4 GM subscript straight p straight m over denominator straight D subscript straight P superscript 2 end fraction
straight F space equals ma
Acceleration space due space to space gravityy
straight a space equals space straight F over straight m space equals space fraction numerator 4 GM subscript straight P over denominator straight D subscript straight P superscript 2 end fraction