A shaft carries a weigh \(W\) at the centre. The \(C G\) of the weight is displaced by an amount \(e\) from the axis of the rotation. If \(\mathrm{y}\) is the additional displacement of the \(C G\) 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) \(\frac{\omega}{\left[\frac{\omega_{c}}{\omega}\right]^{2}-1}\).