question_answer

A wheel is rolling straight on ground without slipping. If the centre of mass of the wheel has speed v, the instantaneous velocity of a point P on the rim, defined by angle \[\theta ,\] 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)    \[v\,sin\left( \frac{\theta }{2} \right)\]            

D)        \[v\,(sin\,\theta )\]

Correct Answer: B

Solution :

[b] \[{{v}_{p}}=\sqrt{{{v}^{2}}+{{v}^{2}}+2{{v}^{2}}\cos \theta }=\sqrt{2{{v}^{2}}(1+\cos \theta )}\] \[=2v\,\cos \theta /2\]