question_answer

Two putty balls of equal mass moving with equal velocity in mutually perpendicular directions, stick together after collision. If the balls were initially moving with a velocity of \[45\sqrt{2}\,m{{s}^{-1}}\] each, the velocity of their combined mass after collision is          [Haryana CEE 1996; BVP 2003]

A)             \[45\sqrt{2}\,m{{s}^{-1}}\]

B)               \[45\,m{{s}^{-1}}\]

C)             \[90\,m{{s}^{-1}}\]

D)               \[22.5\sqrt{2}\,m{{s}^{-1}}\]

Correct Answer: B

Solution :

    Initial momentum             \[\vec{P}=m45\sqrt{2}\ \hat{i}+m45\sqrt{2}\ \hat{j}\]Þ \[|\vec{P}|=m\times 90\]             Final momentum \[2m\times V\]             By conservation of momentum \[2m\times V=m\times 90\]             \\[V=45\,m/s\]