question_answer 43)

                  A cricket ball of mass 150 g has an initial velocity \[\vec{u}=\,(3\hat{i}+\,4\hat{j})\,m{{s}^{-1}}\] and a final velocity \[\vec{u}=(3\hat{i}\,\,+\,4\hat{i})\,m{{s}^{-1}}\] and a final velocity \[\vec{v}=\,-(3\hat{i}\,\,+\,4\hat{i})\,m{{s}^{-1}}\] after being hit. The change in momentum (final momentum initial momentum) is (in kg \[m{{s}^{-1}}\]1)                 (a) zero                                (b) \[-\,(0.45\hat{i}\,+\,0.6\hat{j})\]                 (c) \[-\,(0.9\hat{i}\,+1.2\hat{j})\]              (d) \[-5\,(\hat{i}+\,\hat{j})\]

Answer:

                  (c) Change in momentum \[=\,m\,(\vec{\upsilon }\,-\vec{u})\]                 \[=\,\frac{150}{1000}\,\,(-3\hat{i}\,-4\hat{j}\,-3\hat{i}\,-4j)\]                 \[=0.15\,(-6\hat{i}-16\hat{j})=-\,(0.9\hat{i}\,+1.2\,\hat{j})\]