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Gravitation question

2012 · Q152
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Gravitation question

2012 · Q152

NEETPhysicsGravitationMCQ+4 / −1
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
  1. A
    4GMPDP2{{4G{M_P}} \over {D_P^2}}DP2​4GMP​​
  2. B
    GMPmDP2{{G{M_P}m} \over {D_P^2}}DP2​GMP​m​
  3. C
    GMPDP2{{G{M_P}} \over {D_P^2}}DP2​GMP​​
  4. D
    4GMPmDP2{{4G{M_P}m} \over {D_P^2}}DP2​4GMP​m​
View written solutionFree

Correct answer: A

Gravitational attraction force on particle B,

Fg=GMPm(DP/2)2{F_g} = {{G{M_P}m} \over {{{\left( {{D_P}/2} \right)}^2}}}Fg​=(DP​/2)2GMP​m​

Acceleration of particle due to gravity

a=Fgm=4GMPDP2a = {{{F_g}} \over m} = {{4G{M_P}} \over {D_P^2}}a=mFg​​=DP2​4GMP​​

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