Eashan1337

Question: Two small spheres, each having a mass of 20 g, are suspended from a common point by two insulating strings of length 40 cm each. The spheres are identically charged and the separation between the balls at equilibrium is found to be 4 cm. find the charge on each spheres. What I have done: Given, m = 20 g distance between the balls = 0.04 m length of strings = 0.4 m After making a free body diagram, I got two equations. Tcosθ = F (electrostatic force) Tsinθ = mg Dividing the two, tanθ = mg/F - (i) Now, looking at the triangle made in the figure, I dropped a perpendicular from the vertex from where the two strings are joined. Looking at the new right angled triangle, I found the length of the perpendicular. It comes out to be 0.3994. So, tanθ = 0.3994/0.02 = 19.97 Now looking at the equation (i), I put the value of tanθ. Therefore, F = mg/19.97. I'm taking g = 10m/s² F = 10(20)/19.97 F= 10.015 (9 x 10⁹ x Q²)/0.0016 = 10.015 Q² = 1.78 x 10⁻¹² Q = 1.334 x 10⁻⁶ Well, that's what my answer comes, but it's wrong. Can someone guide me where I got it wrong?

I need to simplify cos⁻¹[(2x - 3√(1 - x²))/(√13)] Any ideas to how to do so?