Two small balls of mass m , bearing a charge q each , are connected by a nonconducting thread of length 2 ℓ . At a certain instant, the middle of the thread starts moving at a constant velocity v perp

Question

Two small balls of mass m , bearing a charge q each , are connected by a nonconducting thread of length 2 ℓ . At a certain instant, the middle of the thread starts moving at a constant velocity v perpendicular to the direction of the thread at the initial instant. Determine the minimum distance d between the balls. (Take v = 1 cm / s , ℓ = 9 m , m = 1 kg , q = 1 μ C )

TestHub · Accepted Answer

Looking from COM reference frame

initial energy $= \frac{1}{2} (2 m) v^{2} + \frac{Kqq}{2 ℓ}$ final energy $= 0 + \frac{Kqq}{d}$ so, conservation of energy : $mv^{2} + \frac{Kq ^{2}}{2 ℓ} = \frac{Kq ^{2}}{d}$ Solving for d, we get $d = 15.00$

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