Question

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

• A. the rope will slack when, $T=mgcos\left(\theta \right)$ .
• B. the rope will slack when, $\frac{m{v}^{{}^{\prime }2}}{r}>mgcos\left(\theta \right)$ .
• 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, $\frac{m{v}^{{}^{\prime }2}}{r}=mgcos\left(\theta \right)$ .

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 $(mgcos\left(\theta \right))$ .
$\Rightarrow \frac{m{v}^2}{r}=mgcos\left(\theta \right)$
$\Rightarrow$ At the very next moment,
$mgcos\left({\left(\theta \right)}^{{}^{\prime }}\right)<\frac{m{v}^2}{r}$ .
So, the rope will leave the circular path.