Question

A bead moves outwards with constant speed ‘u’ along the spoke of a wheel and wheel rotating about its axis with constant angular velocity ‘ω’. The bead leaves the centre of the wheel at t = 0. The velocity of the bead as a function of time is given by (where ${\hat{e}}_r$ and ${\hat{e}}_t$ are unit vectors along radial and tangential directions, respectively)

• A. $-u{\hat{e}}_r$
• B. $u{\hat{e}}_r+\left(utw\right){\hat{e}}_t$
• C. $u{\hat{e}}_r+uw{\hat{e}}_t$
• D. $utw{\hat{e}}_t$

Answer 1

The correct option is B $u{\hat{e}}_r+\left(utw\right){\hat{e}}_t$



The situation is as shown in the figure. At any time `t` its location is described by two parameters –r i.e, the distance from centre and $\theta$, the angle rotated by spoke in time `t`.
Velocity of bead at time t, $\overrightarrow{v}=u{\hat{e}}_r+r\omega {\hat{e}}_t$
Where ${\hat{e}}_r\&{\hat{e}}_t$ one unit vectors along radial and tangential directions
$\therefore \overrightarrow{v}=u{\hat{e}}_r+\left(ut\right)w{\hat{e}}_t$ where r = ut as $\frac{dr}{dt}=u$