Question

A bead of weight w can slide on the smooth circular wire in a vertical plane. The bead is attached by a light thread to the highest point of
the wire and in equilibrium, the thread is taut and make an angle $\theta$ with the vertical, then the tension of the tread and reaction of the wire on the bead are

• A. $T=W\cos \theta R=W\tan \theta$
• B. $T=2W\cos \theta R=W$
• C. $T=W\cos \theta R=W\sin \theta$
• D. $T=W\sin \theta R=W\cot \theta$

Answer 1

The correct option is B $T=2W\cos \theta R=W$

$\begin{array}{c}UseLAM{I}^{\prime }sTHEOREM\\ \frac{T}{\sin 2\theta }=\frac{R}{\sin \left(\pi -2\theta +\theta \right)}\\ \Rightarrow \frac{W}{\sin \left(\pi -\theta \right)}\\ \frac{T}{\sin 2\theta }=\frac{R}{\sin \theta }=\frac{W}{\sin \theta }\\ R=WandT=2W\cos \theta \end{array}$