Question

Determine the minimum speed at the topmost point of a vertical circle of radius \(L\) for the string to remain taut.

• A. \( \sqrt{gL} \)
• B. \( \sqrt{2gL} \)
• C. \( \sqrt{3gL} \)
• D. \( gL \)

Hint:

In vertical circular motion, the minimum speed at the top occurs when the tension becomes zero. Then the centripetal force is provided only by the weight \(mg\).

Answer 1

The Correct Option is A

Concept: For a body moving in a vertical circle, the centripetal force at the topmost point is provided by the tension in the string and the weight of the body. \[ \frac{mv^2}{L} = mg + T \] For the string to remain just taut, the minimum condition occurs when the tension becomes zero.

Step 1: Apply the minimum tension condition \(T = 0\). \[ \frac{mv^2}{L} = mg \]

Step 2: Solve for the speed \(v\). \[ v^2 = gL \] \[ v = \sqrt{gL} \] Thus, the minimum speed required at the topmost point is \[ \boxed{\sqrt{gL}} \]