A point object of mass m is connected to an inertialess string of length L, the other end of which is connected to a fixed point O. At time t=0, the object is assumed to move horizontally in a vertical plane from the bottom point A (OA=L). in the clockwise direction with an initial speed v0 as seen in the figure.
If √2gl<v0<√5gl, then at a point B (the angle between OB and the horizontal direction is designated θ) the magnitude of the force acting on the object from the string becomes zero, where OB=L and the velocity is perpendicular to OB. v being the magnitude of the vector velocity. If 0<θ<pi
1) the speed v is given by....?
2) the initial speed is ....?
3) From the point B, for a while, the object takes a parabolic orbit till C where OC=L . The maximum elevation (with respect to location B) is expressed as ....?
4) In the case θ=pi/3, the angle ϕ measured as in fig. specifying the point C becomes. .....?
5) and finally the angle , the angle between the object velocity at the point C and the horizontal direction is ...?
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