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. `(3 mv)/T`
D. None of these

Answer

B

Explanation

Average force = `("change in m cm entum")/("time") = (m v//2 - (mv))/(T) = (3 mv)/(2T)`.