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A U-shaped wire has a rough semicircular bending between A and B as shown in the figure. A bead of mass m moving with uniform speed v through the wire enters the semicircular bend at A and leaves at B with velocity v/2 after time T. The average force, exerted by the bead on the part AB of the wire is

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a

mv2T

b

3mv2T

c

3mvT

d

none of these

answer is B.

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Detailed Solution

The momentum of the bead at A is p→i=−mvi^The momentum of the bead at B p→f=(mv/2)i^Therefore, the magnitude of the change in momentum between A and B is Δp=p→f−p→i=(3/2)mvAverage force exerted by the bead on the wire isFav=ΔpΔt=3mv2T

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A U-shaped wire has a rough semicircular bending between A and B as shown in the figure. A bead of mass m moving with uniform speed v through the wire enters the semicircular bend at A and leaves at B with velocity v/2 after time T. The average force, exerted by the bead on the part AB of the wire is