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The bob of a pendulum has mass m = 1kg and charge q = 40 $μ C$ . Length of pendulum is l = 0.9m. The point of suspension also has the same charge 40 $μ C$ . What is the minimum speed u (in m/s) should be imparted to the bob so that it can complete vertical circle?

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answer is 6.

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Detailed Solution

In the given problem which should first determine wether string can get slack or net.

As $\frac{{kq}^{2}}{ℓ^{2}} > mg$ string will no slack for any value of a. Thus now from conservation of energy, we get network done by electric force is zero $\frac{1}{2} {mu}^{2} = mg (2 ℓ) \Rightarrow u = \sqrt{4 g ℓ} = 6 m / s$

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