question_answer

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) \[2v\,\sin \,(\theta /2)\]   

B) \[v\,\sin \,\theta \]

C) \[2v\,\cos \,(\theta /2)\]  

D) \[v\,\cos \,\theta \]

Correct Answer: A

Solution :

[a]  \[{{v}_{p}}=\sqrt{{{v}^{2}}+{{v}^{2}}+2vv\cos (180-\theta )}\] \[\Rightarrow {{v}_{p}}=\sqrt{2{{v}^{2}}[1-cos\theta ]}\] \[=2v\sin (\theta /2)\]