word problem please help

Question

the gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25lb when the masses are 4ft apart what is the attraction when the masses are 6ft apart?

 

I got 1lb but want to make sure

Answer 1

We know that Force = (M1 x M2 ) / d²

 

We are given that F₁ = 2.25lb, and that d₁ = 4f; so the formula becomes 2.25lb = (M1 x M2) / (4f)²

rewriting, we get 2.25lb x 16f² = M1 x M2

 

We are asked to determine F₂ when d₂ = 16f; so the formula becomes F₂ = (M1 x M2) / (6f)²

rewriting, we get F₂ x 36f² = M1 x M2

 

since the masses are the same, we combine the formulas to get 2.25lb x 16f² = 36f² x F₂

 

solving for F₂, we get (2.25lb x 16f²) / 36f²

 

the value for F is 1.0lb