Four balls, each with mass m, are connected by four nonconducting strings to from a square with side with A, as shown in (Fig. 3.43.) The assembly is placed on a horizontal nonconducting frictionless surface. Balls 1 and 2 each have charge q, and balls 3 and 4 are uncharged. Find the maximum speed of balls 1 and 2 after the string connecting them is cut.
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Explanation

Take the illustration presented with the problem as an initial picture. No external horizontal forces act on the set of four balls, so its center of mass stays fixed at the location of the center of the square. As the charged balls 1 and 2 swing out and away from each other, balls 3 and 4 move up with equal y- components of velocity. The maximum - kinetic energy point is illustrated. System energy is conserved, so
`(k_e q^2)/a = (k_e q^2)/(3 a) + (1)/(2) m v^2 + (1)/(2) m v^2 + (1)/(2)m v^2 + (1)/(2)m v^2`
or `(2 k _eq^2)/(3a) = 2 mv^2` or `v = sqrt((k_e q^2)/(3 a m))`.
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