What is the minimum horizontal speed given to the bob of a simple pendulum of length 50 cm so that it describes a complete circle? (Take \(g = 10\ m/s^2\))
\(5\ m/s\)
For a bob tied to a string to just complete a vertical circle, the minimum speed at the lowest point is given by \(v_{bottom} = \sqrt{5gL}\) (obtained from the condition \(v_{top} = \sqrt{gL}\) at the top, combined with energy conservation).
Here \(L = 0.5\ m\) and \(g = 10\ m/s^2\), so \(v_{bottom} = \sqrt{5 \times 10 \times 0.5} = \sqrt{25} = 5\ m/s\). Hence option (a) is correct.
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