question_answer

A wheel is rolling straight on ground without slipping. If the axis of the wheel has speed v, the instantaneous velocity of a point P on the rim, defined by angle \[\text{ }\!\!\theta\!\!\text{ }\], relative to the ground will be '       

A) \[v\cos \left( \frac{1}{2}\theta  \right)\]                       

B) \[2v\cos \left( \frac{1}{2}\theta  \right)\]

C) \[v(1+\sin \theta )\]                 

D) \[v(1+\cos \theta )\]

Correct Answer: B

Solution :

\[\sqrt{{{v}^{2}}+{{v}^{2}}+2{{v}^{2}}\cos \theta }\] \[=\sqrt{2{{v}^{2}}(1+\cos \theta )}=2v\cos \frac{\theta }{2}\]