Question

For vertical circular motion, if $v_{\text{lowermost point}} < \sqrt{5 r g}$ , then,

• A. the rope will slack when, $T=mgcos\left(\theta \right)$ .
• B. the rope will slack when, $\frac{m v^{' 2}}{r}>mgcos\left(\theta \right)$ .
• C. the rope will slack when, $\frac{m v^{2}}{r} < mgcos\left(\theta \right)$ .
• D. the rope will leave the circular path at the very next moment when, $\frac{m v^{' 2}}{r}=mgcos\left(\theta \right)$ .

Answer 1

Answer: (D)

When the rope slacks, then tension in rope is, $T=0$ .
$\Rightarrow $ At this moment, the required centripetal force $\left(F_{C}\right)$ is provided by $\left(\right.mgcos\left(\theta \right)\left.\right)$ .
$\Rightarrow \frac{m v^{2}}{r}=mgcos\left(\theta \right)$
$\Rightarrow $ At the very next moment,
$mgcos\left(\left(\theta \right)^{'}\right) < \frac{m v^{2}}{r}$ .
So, the rope will leave the circular path.