I'm stuck on this problem: A small sphere is attached to a fixed point by a string of length =30cm , and whirls round in a vertical circle under the action of gravity at such speed that the tension in the string when the sphere is at its lowest point is three times the tension when the sphere is at its highest point. From: https://isaacphysics.org/questions/sphere_under_gravity I initially thought it would be constant velocity but that produces the wrong answer and after looking at the hints, I found the velocity at the top is different to the velocity at the bottom. I've tried using ideas of energy where the Energy at the top=mg0.6+0.5mv2 and Energy at the bottom= 0.5mv2 Also, resolving forces: At the top F=T+mg where F is the centripetal force. At the bottom F=3T-mg. I've also tried working out the minimum velocity required using a=v2/r where a=9.81 and r=0.3m. I've tried to use Work=forcexdisplacement so F=W/d and d=0.6 and W=energy at the top or W= energy at the bottom, to produce 2 separate equations. Still stuck.