To solve the equation [tex]\(\frac{15}{\pi r_1^2}=\frac{F_2}{\pi (16 r_1^2)}\)[/tex], follow these steps:
1. Simplify the constants in the equation:
Starting with the given equation:
[tex]\[
\frac{15}{\pi r_1^2} = \frac{F_2}{\pi (16 r_1^2)}
\][/tex]
2. Cancel out the common terms:
Since [tex]\(\pi r_1^2\)[/tex] appears in both denominators, we can cancel them out for simplicity:
[tex]\[
\frac{15}{r_1^2} = \frac{F_2}{16 r_1^2}
\][/tex]
3. Multiply both sides by [tex]\(r_1^2\)[/tex] to eliminate the [tex]\(r_1^2\)[/tex] terms:
Multiplying both sides by [tex]\(r_1^2\)[/tex] results in:
[tex]\[
15 = \frac{F_2}{16}
\][/tex]
4. Isolate [tex]\(F_2\)[/tex]:
To solve for [tex]\(F_2\)[/tex], multiply both sides of the equation by 16:
[tex]\[
15 \times 16 = F_2
\][/tex]
5. Perform the multiplication:
Calculating the left-hand side:
[tex]\[
15 \times 16 = 240
\][/tex]
6. Write the final solution:
Hence, the value of [tex]\(F_2\)[/tex] is:
[tex]\[
F_2 = 240
\][/tex]
This gives us the result:
[tex]\[
\boxed{240}
\][/tex]
