Q.A stone of mass $0.5\ \text{kg}$ tied to a string of length $1\ \text{m}$ is whirled in a vertical circle. Find

Given: mass $m=0.5\ \text{kg}$ (does not affect either minimum speed), radius $r=1\ \text{m}$, $g=9.8\ \text{m/s}^2$.

(a) Minimum speed at the top. At the critical (minimum-speed) condition, the string tension just becomes zero and gravity alone supplies the required centripetal force: $mg = \frac{mv_{\text{top,min}}^2}{r} \quad\Longrightarrow\quad v_{\text{top,min}} = \sqrt{gr} = \sqrt{9.8 \times 1} = \sqrt{9.8} \approx 3.13\ \text{m/s}$ …

Set tension to zero at the top to find $v_{\text{top,min}}=\sqrt{gr}$, then use conservation of mechanical energy across the …

• Forgetting the height difference between top and bottom is $2r$ (the diameter), not $r$. …