A slender shaft supported on two bearing at its ends carries a disc with an eccentricity \(e\) from the axis of rotation. The critical speed of the shaft is \(N\). If the disc is replaced by a second one of same weight but mounted with an eccentricity \(2 e\), critical speed of the shaft in the second case is

(a) \(1 / 2 \mathrm{~N}\)

(b) \(1 / \sqrt{2} N\)

(c) \(N\)

(d) \(2 \mathrm{~N}\)