question_answer

A disc is rolling (without slipping) on a horizontal surface. C is its centre and Q and P are two points equidistant from C. Let \[{{\nu }_{p}},\,\,{{\nu }_{Q}}\,and\,{{\nu }_{C}}\] be the magnitudes of velocities of points P, Q and C respectively, then

A)  \[{{v}_{Q}}> {{V}_{C}} > {{V}_{P}}\]        

B)  \[{{v}_{Q}}< {{V}_{C}} < {{V}_{P}}\]

C)  \[{{v}_{Q}}= {{v}_{P}}, \,{{v}_{C}}= \frac{1}{2}{{v}_{P}}\]         

D)  \[{{\operatorname{v}}_{Q}}< {{V}_{C}} > {{V}_{P}}\]

Correct Answer: A

Solution :

The rolling (without slipping) about O is shown in figure. From figure \[OQ > OC >OP\] We know that, \[v = r\,\,\omega \] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{V}_{Q}}> {{V}_{C}} > {{V}_{P}}\]