1.

A long horizontal rod has which can slide along its length, and initially placed at a distance L from one end A of the rod. The rod is set in angualar motion about A with constant angular acceleration a. If the coefficient of friction between the rod and the bead is m, and gravity is neglected, then the time after which the bead starts slipping is :

Answer»

infinitesimal
`(MG)/(4)`
`(mg)/(2)`
`mg(1-mu)`

Solution :Here centripetal force for the bead is PROVIDED by friction `F = mu(Fomega)/(t) a_(t)` where `a_(t) `=tangential ACCELERATION and `a_(t) =(upsilon)/(t)`
L = distance of point :. linear speed `upsilon = Lomega`
HENCE `F= mum (L omega)/(t). mLomega^(2)= mum (Lomega)/(t)`
`omega=(mu)/(t)`
`t=(mu)/(omega)`But=`alpha.t`
`:.t=(mu)/(alphaxxt)`
or `t^(2)=(mu)/(alpha)`
and `t=sqrt(mu)/(alpha)`
Hence choice is (a)


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