A `U`-shaped wire has a semicircular bending between `A` and `B` as shown in Fig. A bead of mass `m` moving with uniform speed `v` through a 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

Options

A. `0`
B. `(3mv)/(2T)`
C. `(3mv)/T`
D. none of these

Answer

B

Explanation

The momentum of the ead at `A` is `P_(i)-mvhati`

The momentum of the bead at `B` is `vecP_(f)=((mv)/2)hati`
Therefore, the magnitude of the change in momentum between `A` and `B` is
`/_\P=|vecP_(f)-vecP_(f)|=(3/2)mv`
Average force exerted by the bead on the wire is
`F_(av)=(/_\p)/(/_\t)=(3mv)/(2T)`