Question

A small ball is tied to a light inextensible thread of length \(64\,cm\) and is whirled in a vertical circle. If the thread is just taut at the highest point of the circle, then the minimum speed of the ball at the lowest point is: (Take \(g=10\,m/s^{2}\))

• A. \(2.53\,m/s\)
• B. \(5.66\,m/s\)
• C. \(8.0\,m/s\)
• D. \(10.0\,m/s\)

Hint:

For vertical circular motion, remember: \[ \boxed{ v_{\text{top(min)}}=\sqrt{gr} } \] and \[ \boxed{ v_{\text{bottom(min)}}=\sqrt{5gr} } \] These two formulas are among the most frequently used results in vertical circle problems.

Answer 1

The Correct Option is B

For a conical pendulum, $T\cos 60° = mg$ and $T\sin 60° = mv^2/r$, so $\tan 60° = v^2/(rg)$. With $r = L\sin 60° = 0.64 \times (\sqrt{3}/2) \approx 0.554$ m, the speed is $v = \sqrt{rg\tan 60°} \approx 3.1$ m/s.