Four identical pendulums are made by made by attaching a small ball of mass 100 ~g on a 20 ~cm long thread and suspended from the same point. Now each ball is given charge Q so that balls move away from each other with each thread making an angle of 45^ from the vertical. The value of Q is close to ( 1 4 ₀ =9 10⁹ . in SI units).

Step-by-step solution

From the diagram, ( OA = L / 2 ) AC = BC = L AD = L 2 Net electrical force on charge (A ) is: array l F = F _ AD + F _ AB 45^ + F _ AC 45^ F = Q ² 4 _ o 2 ~L ² + Q ² 4 _ o L ² 2 + Q ² 4 _ o L ² 2 ~F = 2 Q ² 16 _ o L ² (2 2 +1) array Perpendicular to the string, net force is zero. ( F 45^ = mg 45^ ) array l 2 Q ² 16 ₀ ~L ² (2 2 +1)= mg Q =1.61 10⁻⁶ C array