To determine the charge on the other vinyl balloon, let's use Coulomb's Law, which states that the electric force [tex]\( F \)[/tex] between two charges [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] separated by a distance [tex]\( d \)[/tex] is given by:
[tex]\[ F = k \frac{q_1 q_2}{d^2} \][/tex]
We need to solve the problem step by step to find [tex]\( q_2 \)[/tex]. Let's start by rearranging the formula to solve for [tex]\( q_2 \)[/tex]:
[tex]\[ q_2 = \frac{F d^2}{k q_1} \][/tex]
We are given the following values:
- [tex]\( F = 3.0 \times 10^{-3} \)[/tex] newtons
- [tex]\( d = 6.0 \times 10^{-2} \)[/tex] meters
- [tex]\( q_1 = 3.3 \times 10^{-8} \)[/tex] coulombs
- [tex]\( k = 9.0 \times 10^9 \)[/tex] newton-meter[tex]\(^2\)[/tex] per coulomb[tex]\(^2\)[/tex]
Now, let's substitute these values into our rearranged equation:
[tex]\[ q_2 = \frac{(3.0 \times 10^{-3}) \cdot (6.0 \times 10^{-2})^2}{(9.0 \times 10^9) \cdot (3.3 \times 10^{-8})} \][/tex]
Performing the calculations step-by-step:
1. Calculate [tex]\( d^2 \)[/tex]:
[tex]\[
d^2 = (6.0 \times 10^{-2})^2 = 3.6 \times 10^{-3}
\][/tex]
2. Multiply [tex]\( F \)[/tex] by [tex]\( d^2 \)[/tex]:
[tex]\[
F \cdot d^2 = (3.0 \times 10^{-3}) \cdot (3.6 \times 10^{-3}) = 1.08 \times 10^{-5}
\][/tex]
3. Multiply [tex]\( k \)[/tex] by [tex]\( q_1 \)[/tex]:
[tex]\[
k \cdot q_1 = (9.0 \times 10^9) \cdot (3.3 \times 10^{-8}) = 2.97 \times 10^2
\][/tex]
4. Divide the results from step 2 by step 3:
[tex]\[
q_2 = \frac{1.08 \times 10^{-5}}{2.97 \times 10^2} = 3.636363636363636 \times 10^{-8}
\][/tex]
Thus, the charge on the other vinyl balloon [tex]\( q_2 \)[/tex] is:
[tex]\[ q_2 \approx 3.6 \times 10^{-8} \text{ coulombs} \][/tex]
So, the correct answer is:
B. [tex]\( 3.6 \times 10^{-8} \)[/tex] coulombs
