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/s²)
- A.5 m/s
- B.7.5 m/s
- C.10 m/s
- D.12.5 m/s
Correct answer
Explanation
The correct answer is A, 5 m/s. To just complete a vertical circle, a bob on a string needs a speed of at least √(5gL) at the lowest point, and √(5 × 10 × 0.5) = √25 = 5 m/s.
A string can only pull, never push. So at the top of the circle the string just goes slack when gravity alone supplies the centripetal force, which means v² at the top equals gL. Going from the top down to the bottom, a fall of 2L, energy conservation adds 4gL, so v² at the bottom must be gL + 4gL = 5gL. Remember to convert 50 cm into 0.5 m before putting it into the formula.
B, 7.5 m/s, would also take the bob round, but it is more than the minimum the question asks for.
C, 10 m/s, and D, 12.5 m/s, are larger still; any speed above 5 m/s completes the circle, so none of them is the least value.
Exam tip: string pendulum, √(5gL) at the bottom and √(gL) at the top; for a rigid rod the bottom speed needs only √(4gL).
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