Sure, let's solve this step by step.
If F is inversely proportional to the square of r, it means we can write the relationship as:
F * r^2 = k
where k is a constant. This constant k remains the same for every pair of F and r in our problem due to the property of inverse proportionality.
1. Calculating the Constant:
Let's substitute F = 50, and r = 3 into the above equation to get the constant k. So:
50 * 3^2 = k
50 * 9 = k
450 = k
So we get the constant k as 450.
2. Finding the New F
We know that F2 * (r2)^2 = k. We know the value of k, and r2 is given as 12. Let's substitute these into the equation to find F2 as follows:
F2 * 12^2 = 450
F2 * 144 = 450
F2 = 450 / 144
So, F2 = 3.125
Hence, the value of F when r is 12 is 3.125.