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A bullet of mass 10 g is fired with speed v at the stationary bob of a simple pendulum. After a head-on collision the bullet rebounds with a speed of 100 m/s. The pendulum has length 0.5 m and its bob has mass 1 kg. If the string is inextensible and g = 10 m/s², find the minimum value of v (in m/s) for which the bob just completes a full vertical circle.

1. 400 m/s
2. 200 m/s
3. 500 m/s
4. 300 m/s

Correct answer: 400 m/s

Solution

The bob needs a minimum bottom speed of sqrt(5gL) = 5 m/s to loop the circle, and momentum conservation (with the bullet reversing) gives v = 400 m/s.

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