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Answer:
A particle of mass m is attached to one end, A, of a light inelastic string of length l. The other end of the string, B, is attached to a ceiling so that the particle is free to swing in a vertical plane. The angle between the string and the downward vertical is θ radians. You may assume that the air resistance on the particle is negligible. Initially, θ=3π​ and the particle is released from rest.
(i) Show that the potential energy lost by the particle since leaving its initial position is 2mgl​(2cosθ−1). Hence find an expression for v2, where v is the linear speed of the particle, in terms of l,g and θ. (ii) Show that the tension in the string at any point of the motion is mg(3cosθ−1). (iii) Find the greatest tension in the string. What is the position of the particle when the tension in the string is greatest?
v2=gl(2cosθ−1) 2mg when θ=0