Question

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 $\nu$ through a wire enters the semicircular bend at $A$ and leaves at $B$ with velocity $\nu /2$ after time. The average force exerted by the bead on the part $AB$ of the wire is:

• A. 0
• B. $\frac{3m\nu }{2T}$
• C. $\frac{3m\nu }{T}$
• D. none of these

Answer 1

The correct option is B $\frac{3m\nu }{2T}$

Momemtum of bead at $A\left(P_{initial}\right)=-mv$

Momemtum of bead at $B\left(P_{final}\right)=\frac{mv}{2}$

Average Force $=F_{avg}=\frac{P_f-P_i}{t}$

$\Rightarrow F_{avg}=\frac{\frac{mv}{2}-(-mv)}{T}$

$=\frac{3mv}{2T}$