Physics
A cyclist leans inwards when he is negotiating a curve so that

His weight may be reduced
No frictional force may be produced between the wheels and the axle
Necessary centripetal force may be available from the horizontal component of the normal reaction due to the track to maintain the curved motion.
He may increase his speed

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Physics
When a pail of water is swung in a vertical circle, the water does not fall out at the top of the loop when the speed is

Above a certain minimum value irrespective of amount of water in the pail
Below a certain minimum value irrespective of amount of water in the pail
Above a certain minimum value depending on amount of water in the pail
Below a certain minimum value depending on amount of water in the pail

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