Question

A particle P of mass m attached to vertical axis by two strings AP and BP of length l each. The separation AB=l. The point p rotates around the axis with an angular velocity $\omega$. the tension in two strings are $T_1$ and $T_2$
taut only if $\omega >\sqrt{\frac{2g}{l}}$

• A. $T_1$= $T_2$
• B. $T_1$+ $T_2$=$\frac{2}{\sqrt{3}}m{\omega }^{2}l$
• C. $T_1$- $T_2$=2mg
• D. BP will remain

Answer 1

The correct option is B $T_1$+ $T_2$=$\frac{2}{\sqrt{3}}m{\omega }^{2}l$

From figure in equilibrium, $T_1\cos 60=mg+T_2\cos 60$ here $\theta =60$ for equilateral triangle.
or $T_1\left(1/2\right)=mg+T_2\left(1/2\right)\Rightarrow T_1-T_2=2mg$
also, $T_1\sin 60+T_2\sin 60=m{\omega }^{2}l$
or $T_1+T_2=\frac{2}{\sqrt{3}}m{\omega }^{2}l$