Question

A particle of mass m is attached to one end of a light , inextensible string of length l whose either end is fixed at





c. At lowest point ..The particle is given the minimum velocity to complete a circular path in the vertical ppane as it moves..

Answer 1

Answer:

Vmin =  √gl

Explanation:

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),

mv2/l = T+mg

Putting T=0;

mv2/l = mg;

we get Vmin =  √gl