Final answer:
To calculate the magnitude of the charge required to support the weight of the tape, we can use Coulomb's Law and the force of gravity acting on the tape. By plugging in the known values and solving for the charge, we find that the magnitude of the charge required is 2.76 × 10^7. The correct answer is a) 2.76 X 10^7
Step-by-step explanation:
To calculate the magnitude of the charge required to support the weight of the tape, we need to find the electrostatic force acting on the tape. The electrostatic force can be calculated using Coulomb's Law:
F = k * (q1 * q2) / r^2
Where F is the force, k is the proportionality constant, q1 and q2 are the charges, and r is the distance between the charges.
In this case, the force of gravity acting on the tape is equal to the electrostatic force:
F_gravity = F_electrostatic
By substituting the known values and solving for the charge (q1 or q2), we can find the magnitude of the charge. Plugging in the values, we get:
k * (q * q) / r^2 = m * g
where k is the proportionality constant, q is the magnitude of the charge, r is the distance between the charges, m is the mass of the tape, and g is the acceleration due to gravity. Rearranging the equation, we can solve for the magnitude of the charge:
q = sqrt((m * g * r^2) / k)
Plugging in the known values, we get:
q = sqrt((10.0 mg * 9.8 m/s^2 * (1.00 cm)^2) / k)
Using the given proportionality constant of 2.31 × 10^16 J pm, we can calculate the magnitude of the charge:
q = sqrt((10.0 mg * 9.8 m/s^2 * (1.00 cm)^2) / (2.31 × 10^16 J pm))
Calculating the value, we get q = 2.76 × 10^7. Therefore, the magnitude of the charge required to support the weight of the tape is 2.76 × 10^7.
Therefore, the correct answer is a) 2.76 X 10^7.