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 th

Question

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 $\cos θ = \frac{m}{n}$ , where $m$ and $n$ are smallest integers, then, the value of $m + n$ is

TestHub · Accepted Answer

Let us assume that the length of the string is

l

T - m g \cos θ = \frac{m v^{2}}{l} \dots \dots \dots (i)

m g l \cos θ = \frac{1}{2} m v^{2} - \frac{1}{2} m v_{0}^{2} \dots \dots \dots (i i)

T = 2 m g \dots \dots \dots (i i i)

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