1.

A weight is suspended from a thread of length l. What is the initial speed that has to be imparted to it at the lowest point to make it complete a full revolution? The mass of the thread is to be neglected.

Answer»


Solution :The speed of the weight at the uppermost point should be such that the tension of the thread T and the force of GRAVITY impart to it the necessary CENTRIPETAL acceleration (see FIG )
mg + T = `mv^2//l`
To find the minimum speed at the uppermost point , put T = 0.
We have
`mg = mv^2 "min"//l " or " v^2 min = 2gl`
Taking the potential energy to be zero at point O(the axis of rotation) we obtain ACCORDING to the law of conservation of energy
`(mv_0^2)/(2) -MGL = (mv^2min)/2 +mgl`
Hence `v_(0) ge sqrt(5gl)`


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