question_answer

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

A) the momentum changes by \[m\upsilon \]

B) the momentum changes by \[2m\upsilon \]

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

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

Correct Answer: B

Solution :

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