question_answer

A particle is moving in a circle with uniform speed\[v\]. In moving from a point to another diametrically opposite point,

A)  the momentum changes by\[mv\]

B)  the momentum changes by 2\[mv\]

C)  the kinetic energy changes by (1/2)\[m{{v}^{2}}\]

D)  the kinetic energy changes by\[m{{v}^{2}}\]

Correct Answer: B

Solution :

                Initial velocity \[{{v}_{1}}=v\] Final velocity \[{{v}_{2}}=-\,v.\] Initial momentum \[{{p}_{1}}=mv\] Final momentum \[{{p}_{2}}=m\,(-v)=-\,mv\] Change in momentum \[\Delta p={{p}_{1}}-{{p}_{2}}\] \[=mv-(-mv)\] \[=2\,mv\]