Question 1189966
<br>
The mass is 1/4 as much; since the force of attraction varies directly as the mass, it goes down by a factor of 1/4.<br>
The distance is 3 times as great; since the force varies inversely as the square of the distance, it goes down by a factor of 1/3^2 = 1/9.<br>
ANSWER: (100)(1/4)(1/9) = 100/36 = 25/9 Newtons<br>
Formally....<br>
(1) Find the constant of variation using the known data<br>
{{{F=k(m/d^2)}}}
{{{100=k(8/25)}}}
{{{k=100(25/8)=2500/8=625/2}}}<br>
(2) Use the constant with the new data<br>
{{{F=(625/2)(2/(15^2)) = (625/2)(2/225)=625/225=25/9}}}<br>
ANSWER (the same, of course): 25/9 Newtons<br>