Question

A particle is moving in a circle of radius r with a constant speed v.If time of revolution is T then magnitude of average acceleration in time interval it subtends angle 60 at centre.

Answer 1

$$\begin{gathered} Aftersunbstenedanangle60degree. \\ componentofvelocityininitialdirectionisv\cos 60=v/2 \\ componentinydirection=v\sin 60=\sqrt{3}v/2 \\ accelerationinxdirectionischangeinvelocity/time \\ timetakentosubstendanangle360degreeisT. \\ for60degree,\frac{T}{6} \\ accelerationisxdiecrection=\frac{v-v/2}{T/6} \\ {a}_x=3v/T \\ ycomponent \\ {a}_y=\sqrt{3}v/2/T/6=3\sqrt{3}v/T \\ a=\sqrt{{a_x}^2+{a_y}^2} \\ a=\sqrt{9+27}v/T \\ a=6v/T \end{gathered}$$