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Two small metallic spheres, cach of mass $m=0.20 \mathrm{g},$ are suspended as pendulums by light strings from a common point as shown in Figure P15.15. The spheres are given the same electric

charge, and it is found that they come to equilibrium when each string is at an angle of $\theta=5.0^{\circ}$ with the vertical. If each angle of $\theta=5.0^{\circ}$ with the vertical. If each

string has length $L=30.0 \mathrm{cm},$ what is the magnitude of the charge on each sphere?

7.22 $\mathrm{nC}$

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um here we have opposed to why exists? Well, two axes and, uh, it's making an angle here. The four so far mg is acted on there. Particle. There's a force off Effie in this direction. And the force, which is cool to detention, is acted here of making an angle of five degrees. So summing up the forces in my direction with physical zero, we can write mg will be cool to Ah, they were total component off the tension. So the vertical component off the attention will be this one here, which is a tension t t course, uh, t cause five degrees. Where is the sum of forces in X direction that easy in this direction. This will be, uh, attention. Sorry. T of sign signed five D, please. This will be called to F e. So, um, if he is equal to t sign five degrees, then we can right f e. If he you will be equal to M G if he's called NGO ever cost later. With just five degrees sign five degrees. We, uh, sold 40 from this equation. Let's call this one. And then we just replaced the value off a tee with MG cause five degrees. This equation becomes the MG Day five Giddens, The distance separating the tooth fairy is ah from the figures are tickled to l sign five degrees. From there we can write if e mg 10 5 degrees, we'll be equal Thio, this will be a k e kills where kun squared divided by to l signed five degrees square. This is the distance s So this will be called M g m g eating five Guineas. So Kay is actually caused him. So this should be a very small then from here we can solve for a queue and queue will be equal to two l sign five degrees into mg 10 5 degrees divided by Okay, so let me just write your cage escape. Hey, just is a constant K um then substituting values we get here two times zero point Crete. I'm signed. Five agrees into into square root off 0.2 times Sent about minus three times 9.8 time staying five degrees divided by 8.99 times 10 to the power Fine is already okay then the k the charge we get finally charge will be cool too If you charge will be called to 7.2 then I'm cool. This is our answer