Two point mass m are connected the light rod length i and is free to roatate in vertical plane as shown. Calculate the minimum horizontal velocity is given to mass so that it completes the circular motion in
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 mv2l=T−mgcosθ⟹(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 mv2l=T−mg
When the object is at the top most position C, θ = π, hence
centripetal force mv2l=T+mg
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=√gl
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 mv2l=T−mgcosθ⟹(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 mv2l=T−mg
When the object is at the top most position C, θ = π, hence centripetal force mv2l=T+mg
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=√gl
