Question

Figure shows a bead of mass m moving with uniform speed v through a U- shaped smooth wire. The wire has a semi-circular bending between A and B. The average force exerted by the bead on the part AB of the wire is –

• A. 2 mv
• B. $\frac { \pi \mathrm { d } } { 2 }$
• C. $\frac { \pi \mathrm { d } } { 2 \mathrm { v } }$
• D. $\frac { 4 \mathrm { mv } ^ { 2 } } { \pi \mathrm { d } }$

Answer 1

Answer: (D)

$\frac { 4 \mathrm { mv } ^ { 2 } } { \pi \mathrm { d } }$

Answer 2

Change in momentum = 2mv

time = $\frac { \pi \mathrm { d } / 2 } { \mathrm { v } }$ = $\frac { \pi \mathrm { d } } { 2 \mathrm { v } }$

Average force = $\frac { 2 \mathrm { mv } } { \frac { \pi \mathrm { d } } { 2 \mathrm { v } } }$ = $\frac { 4 \mathrm { mv } ^ { 2 } } { \pi \mathrm { d } }$