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A particle of mass m is fixed to one end of a light rigid rod of length l and rotated in a vertical circular path about its other end .The minimum speed of the particle at its highest pt must be

Asked by m.nilu 22nd August 2018, 12:53 PM
Answered by Expert
when an object of mass m which is fixed to an end of an inextensible and light rod
and revolving around a circular path about the other end,
weight of the object and tension in the rod are getting adjusted to provide centripetal force as shown in figure,
Let us consider when the object is at B, as shown in figure.
Centripetal force mv2/l = T - mg cosθ ..............(1)
where T is tension in the rod, m is mass of object and θ is the angular dispalcement
when the vertical position is taken as reference.
When the object is at A, θ = 0. hence centripetal force mv2/l = T - mg
When the object is at the top most position C, θ = π, hence centripetal force  mv2/l = T+mg ............(3)
When the object is at top most position C, minimum required velocity vmin is obtained,
by considering tension in the rod T is zero.
when we apply this condition in eqn.(3), we get vmin =  begin mathsize 12px style square root of g space l end root end style
Answered by Expert 28th August 2018, 11:01 PM
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