Two point masses, each of mass m , are placed a distance d apart and experience a gravitational force F . If 60 % of the mass of one object is transferred to the other, by what percentage must the distance between the masses be decreased so that the gravitational force between them remains F ?

Step-by-step solution

Let the initial mass of each object be m and the distance between them be d . The initial gravitational force is F = G m^2 d^2 . When 60 % of the mass of one object is transferred to the other, the transferred mass is 0.6m . The new masses are m₁ = m - 0.6m = 0.4m and m₂ = m + 0.6m = 1.6m . Let the new distance be d' . To maintain the same force F , we must have: F = G (0.4m)(1.6m) d'^2 = 0.64 G m^2 d'^2 Equating the two expressions for F : G m^2 d^2 = 0.64 G m^2 d'^2 d'^2 = 0.64 d^2 d' = 0.8 d The decrease in dist