The bob of the simple pendulum is given a vertically downward velocity of magnitude v 0 = 5 m s - 1 , as shown in the figure. The string can withstand a maximum tension equal to twice the weight of the bob and during motion the string break

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The bob of the simple pendulum is given a vertically downward velocity of magnitude v 0 = 5 m s - 1 , as shown in the figure. The string can withstand a maximum tension equal to twice the weight of the bob and during motion the string breaks at an angle θ with the vertical. If cos θ = m n , where m and n are smallest integers, then, the value of m + n is

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Correct answer: 5

Let us assume that the length of the string is l T - m g cos ⁡ θ = m v 2 l … … … i m g l cos ⁡ θ = 1 2 m v 2 - 1 2 m v 0 2 … … … i i T = 2 m g … … … i i i ∴ cos ⁡ θ = 1 4 ⇒ m + n = 5

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