Question

A particle $P$ of mass is attached to a vertical axis by two strings $AP$ and $BP$ of length $l$ each. The separation $AB=l$. $P$ rotates around the axis with an angular velocity $\omega$. The tensions in the two strings are $T_1$ and $T_2$

• A. $T_1=T_2$
• B. $T_1=T_2=m{\omega }^{2}l$
• C. $T_1=T_2=2mg$
• D. BP will remain taut only if $\omega \ge \sqrt{\frac{2g}{l}}$

Answer 1

The correct option is D BP will remain taut only if $\omega \ge \sqrt{\frac{2g}{l}}$

$T_{1}sin30=T_{2}sin30+mg$

$T_1-T_2=2mg$

$T_{1}cos30+T2cos30=m{\omega }^2\left(lcos30\right)$

$T_1+T_2=m{\omega }^{2}l$

So, $T_1=m/2({\omega }^{2}l+2g)and{T}_2=m/2({\omega }^{2}l-2g)$

So, option D is correct.