Show that if a uniform heavy right circular cylinder of radius `a` be rotated about its axis, and lais gently on two tough horizontal rails at the same level and distance 2asinβ apart so that the axis of the cylinder is parallel to the rails,the cylinder will remain in contact with both rails if the coefficient of friction μ<tanβ but will initially raise on one rail if μ>tanβ.
1for the cylinder to remain in contact
(N1+N2)cosβ=mg
and (N2-N1)sinβ=μcosβ(N1+N2)
but as N2 and N1>0 N2-N1<mg
hence
μcosβ(mg)<mgsinβ
μ<tanβ
but when μ>tanβ
from the second equation
(N2-N1)sinβ>sinβ(N1+N2)
hence we get
N1<0
but that means one rail has lost contact ...
hence proved
