Question

the speed of a body moving in the circular path of radius r is equal to the speed that it would gain in a free fall by falling through a distance of half of the radius of the circular path. prove that it's centripetal acceleration is equal to the acc due to gravity. what is the direction of velocity and acceleration of an object in uniform circular motion at any instant of time

Answer 1

Dear Student.$$\begin{gathered} ThevelocityoftheUCM\hspace{0.17em}canbecalculatedby. \\ {v}^2=u^2+2as \\ V-velocityofUCMandvelocityoffreefallingfors=r/2. \\ u=0asthisisfreefalling. \\ {v}^2=0+2g\frac{r}{2} \\ \frac{v^2}{r}=g..... \\ DirectionofvelocityisalwaysTangentialanddirectionofaccelerationisalwaysradialtowardscentre, \\ Thisboth\tan gentialandradialmotionresultsincircularmotion. \end{gathered}$$

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