question_answer

A shaft carries a weight W at the centre. The CG of the weight is displaced by an amount e from the axis of the rotation. If 'y is the additional displacement of the CG from the axis of rotation due to the centrifugal force, then the ratio of y to e (where \[{{\omega }_{c}}\] is the critical speed of shaft and \[\omega \] is the angular speed of shaft) is given by:

A) \[\frac{1}{{{\left[ \frac{{{\omega }_{c}}}{\omega } \right]}^{2}}+1}\]              

B) \[\frac{1}{{{\left[ \frac{{{\omega }_{c}}}{\omega } \right]}^{2}}-1}\]

C) \[{{\left[ \frac{{{\omega }_{c}}}{\omega } \right]}^{2}}+1\]                 

D) \[\frac{\omega }{{{\left[ \frac{{{\omega }_{c}}}{\omega } \right]}^{2}}-1}\]