Physics - Circular Motion Question with Solution | TestHub

Geometry: $AP=BP=AB=\ell$, so each string makes $60^{\circ }$ with the vertical axis; radius $r=\ell \sin 60^{\circ }$.

Vertical: $\left(T_1-T_2\right)\cos 60^{\circ }=mg\Rightarrow T_1-T_2=2mg$. (C) true, (A) false.

Radial: $\left(T_1+T_2\right)\sin 60^{\circ }=m{\omega }^2\ell \sin 60^{\circ }\Rightarrow T_1+T_2=m{\omega }^2\ell$. (B) true.

BP taut needs $T_2\ge 0\Rightarrow \omega \ge \sqrt{2g/\ell }$. (D) true.

Answer: B,C,D