A smooth and vertical circular wire frame of radius 2m is fixed inside water as shown. A small bead of specific gravity 0.5 is threaded on the wire and is kept at the origin. If the bead is imparted v

Question

A smooth and vertical circular wire frame of radius 2m is fixed inside water as shown. A small bead of specific gravity 0.5 is threaded on the wire and is kept at the origin. If the bead is imparted velocity V 0 ​ towards positive x axis it moves on the wire frame then neglecting effect of viscosity

TestHub · Accepted Answer

Buoyancy B = ρ w ​ V g = 2 m g (SG 0.5), acting only over the bottom 1 m of the frame that lies inside water. Energy to reach the top (rise 2 R = 4 m): − m g ( 2 R ) + B ( 1 ) = 0 − 2 1 ​ m v 0 2 ​ − 4 m g + 2 m g = − 2 1 ​ m v 0 2 ​ v 0 ​ = 40 ​ = 6.32 m/s

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