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A light, rigid rod is 40.0 cm long. Its top end is pivoted on a frictionless, horizontal axle. The rod hangs straight down at rest with a small, massive ball attached to its bottom end. You strike the ball, suddenly giving it a horizontal velocity so that it swings around in a full circle. What minimum speed at the bottom is required to make the ball go over the top of the circle?

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2.5 m/s

4.0 m/s

3.0 m/s

5.0 m/s

answer is B.

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Detailed Solution

Consider energy conservation of the ball-Earth system between the instant just after you strike the ball and the instant when it reaches the top. The speed at the top is zero if you hit it just hard enough to get it there.

$∆K + ∆U = 0$

$(0 - \frac{1}{2} {mv}^{2}_{i}) + [mg (2 L) - 0] = 0$

$v_{i} = \sqrt{4 gL} = \sqrt{4 (10.0 m / s^{2}) (0.40 m)}$

$v_{i} = 4.0 m / s$

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