question_answer

A wheel is rolling on a plane road. The linear velocity of its centre of mass is v. Then velocities of the point P and Q on the circumference of the wheel relative to road will be                

A)  \[{{E}_{I}}={{E}_{II}}={{E}_{III}}\,and\,\,\,{{E}_{IV}}>{{E}_{V}}\]

B)                  \[\frac{Mgx}{4}\]

C)  \[Mgx\]

D)  \[\frac{Mgx}{2}\]

Correct Answer: D

Solution :

                It is clear from the adjacent diagram                                 \[{{v}_{p}}=v-\omega t=0\]                 \[\Rightarrow \]               \[v=\omega r\] Again       \[{{v}_{Q}}=v+\omega t\]                 \[=\omega t+\omega r=v+v=2v\]