Two 3 kg spherical masses are connected by a 20 m long thread of negligible mass that does not stretch. The masses are charged so they have the same amount of negative charge and the system is hung from the ceiling by the center of the thread.

Determine the charge of each sphere if the angle between the suspended sides of the thread is 17 degree.

The charge of each sphere is  

Explanation:

 The  free body diagram of this question is shown on the first uploaded image  

       From the question we are told that

            The mass of the two sphere is

             The length of the connection is

              The angle between the suspended side is  

At Equilibrium the force acting at the horizontal is  = 0N and the net force acting at the vertical is zero

    This can be represented mathematically as

For  

=>    

   For  

=>  

     Now  

Where F is the electrical force which is mathematically represented as

Therefore

 Where is the distance between the two masses and from the diagram it is

So

making q the subject of the formula  

Where k is  the Coulomb's constant with a value of  

  Substituting values

The negative sign is because we are told from the question that they are negatively charged

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