A wire is bent along an arc with a radius R . A bead is placed on the wire that can move along it without friction. At the initial moment the bead was at point O. The horizontal velocity should be imp

Question

A wire is bent along an arc with a radius R . A bead is placed on the wire that can move along it without friction. At the initial moment the bead was at point O. The horizontal velocity should be imparted to the bead for it to get on to the wire again at point B after flying a certain distance (AB) through the air, will be :-

TestHub · Accepted Answer

At A the bead leaves tangentially with components $(v_{A} cos α, v_{A} sin α)$ and lands at B at the same height. Range along horizontal: $v_{A} cos α \cdot \frac{2 v _{A} s i n α}{g} = 2 R sin α \Rightarrow v_{A}^{2} = \frac{g R}{c o s α}$ . Energy O → A: $\frac{1}{2} v_{0}^{2} = \frac{1}{2} v_{A}^{2} + g R (1 + cos α)$ .

$v_{0}^{2} = g R (2 + 2 cos α + \frac{1}{cos α}) .$

Answer: (A)

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