Question

You are an astronaut, living for a long time interval in the International Space Station (ISS). During your off-duty hours, you have run out of books to read and video games to play. So, your mind wanders to your hobby of music. The last book you read discussed Gauss's law, and you get an inspiration. You plan to attach two nonconducting spheres of radius r = 1.30 cm together using a light insulating string of length L and linear mass density μ = 9.00 ✕ 10⁻³ kg/m, with the string attached at the surface of each sphere. Then, using the electrical system on the ISS, you will be able to electrify each sphere to a charge of Q = 50.0 µC, uniformly spread over the surface of the sphere. The combination will then be allowed to float freely in the ISS. The spheres will repel, creating a tension in the string. When you pluck the string, you wish it to play a perfect middle C, at 262 Hz. Determine the length of the string (in cm) that you need. (Assume the frequency of 262 Hz is the fundamental frequency. Round your answer to at least one decimal place.)

Answer 1