Circular MotionMediumBloom L3
Question
A particle P of mass m 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 ω. The tensions in the two strings are T1 and T2
Options
A.T1 = T2
B.T1 + T2 = mω2l
C.T1 – T2 = 2mg
D.BP will remain taut only if ω ≥ $\sqrt{\frac{2g}{\mathcal{l}}}$
Solution
Sol. $\frac{\sqrt{3}}{2}(T_{1} + T_{2})$= mω2cos30°
T1 + T2 = mω2 ....(i)
T1sin30 – T2 sin30 = mg
T1 – T2 = 2mg ....(ii)
when w increases, T1 increases and T2 decreases
T2 ≥ 0
$\omega \geq \sqrt{\frac{2g}{\mathcal{l}}}$
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