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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2007

  • question_answer
        A particle is acted upon by constant forces\[4\hat{i}+\hat{j}-3\hat{k}\] and\[3\hat{i}+\hat{j}-\hat{k}\] which displace it from a point\[\hat{i}+2\hat{j}+3\hat{k}\]to the point\[5\hat{i}+4\hat{j}+\hat{k}\]. The work done in standard units by the forces is given by

    A)  40                                         

    B)  30

    C)  25                                         

    D)  15

    Correct Answer: A

    Solution :

                    Total force, \[\overrightarrow{F}=(4\hat{i}+\hat{j}-3\hat{k})+(3\hat{i}+\hat{j}-\hat{k})\] \[\overrightarrow{F}=7\hat{i}+2\hat{j}-4\hat{k}\] The particle is displaced from \[A(\hat{i}+2\hat{j}+3\hat{k})\]to\[B(5\hat{i}+4\hat{j}+\hat{k})\] \[\therefore \]Displacement \[\overrightarrow{AB}=(5\hat{i}+4\hat{j}+\hat{k})-(\hat{i}+2\hat{j}+3\hat{k})\] \[=4\hat{i}+2\hat{j}-2\hat{k}\]  Work done\[=\overset{\to }{\mathop{F}}\,.\overset{\to }{\mathop{AB}}\,\] \[(7\hat{i}+2\hat{j}-4\hat{k}).(4\hat{i}+2\hat{j}-2\hat{k})\] \[=28+4+8=40\]unit.


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