Question

A hoop rolls on a horizontal ground without slipping with linear speed $v$. speed of a particle P on the circumference of the hoop at angle $\theta$ is :

• A. $2v\sin \left(\frac{\theta }{2}\right)$
• B. $v\sin \theta$
• C. $2v\cos \left(\frac{\theta }{2}\right)$
• D. $v\cos \theta$

Answer 1

The correct option is A $2v\sin \left(\frac{\theta }{2}\right)$

We know angular velocity $\omega =\frac{linearvelocity}{radius}$ where linear velocity= v and radius R= OP $=2Rsin\frac{\theta }{2}$

Speed of the particle P $={>V}_P=2Rsin\frac{\theta }{2}\left(\frac{V}{R}\right)={>V}_P=2Vsin\frac{\theta }{2}$