Question

A bob of mass m tied to one end of a light string of length 50 cm whirled in a vertical circle. The minimum velocity with which it has to move so that the string remains taut, when it reaches the top most point of the circle is $(g=10\text{ ms}^{-2})$

• A. $10\text{ ms}^{-1}$
• B. $8\text{ ms}^{-1}$
• C. $15\text{ ms}^{-1}$
• D. $5\text{ ms}^{-1}$
• E. $12\text{ ms}^{-1}$

Hint:

Logic Tip: Memorize the critical velocities for vertical circles: Top: $\sqrt{gr}$ Horizontal (midpoint): $\sqrt{3gr}$ Bottom: $\sqrt{5gr}$ If the calculated $v_{top} = \sqrt{10 \times 0.5} = \sqrt{5} \approx 2.23$ is not in the options, the question is asking for the initial launching velocity at the bottom!

Answer 1

The Correct Option is D