Answer :
If the mountain 6 km from the person exerts gravitational force on him then the mass of the mountain is 1.21 × 10¹⁷ Kg . .
it is given that , mountain exerts a gravitational force of the person that is equal to 2.30% of his weight ;
let the person has mass "m" , then its weight is ⇒ w = mg ;
the gravitational force between the person and mountain is :
F = GmM/R² ,
the gravitational force is 2.30% of the weight of person ,
So , 0.023mg = GmM/R² ;
M = 0.023gR²/G ;
so the separation distance (R) = 6 km = 6000 m .
substituting g = 9.8 , R = 6000 and G = 6.673×10⁻¹¹ ;
M = 0.023 × 9.8 × 6000²/6.673×10⁻¹¹ ;
On simplifying above values ,
we get ;
M = 1.21 × 10¹⁷ Kg .
Therefore , the mass of the mountain is 1.21 × 10¹⁷ Kg .
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