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**packer** Small bead mass denoted by m, suspended from fixed point O by a light inextensible string length a. Then set into motion with the string taut at B where B is vertically below O which horizontal speed u.

Given that the string does not become slack, show the least value of u required for the bead to make complete revolutions about O is 5ag^1/2.

I have it to where u^2=v^2 +4ag through using mechanical energy principle but I fail to see how v^2 =ag when v is greater than or equal to 0 for complete revolutions where v is the highest point of the circle.

On the mark shceme they aquired v^2 =ag by stating (mv^2)/a=mg but I thought it should surely be (mv^2)/a=T +mg especially considering the string never becomes slack.

Help please...