RAJASTHAN PMT Rajasthan - PMT Solved Paper-2006

  • question_answer
    If force\[\mathbf{\vec{F}=5\vec{i}+3\vec{j}+4\vec{k}}\]makes a displacement of \[\mathbf{\vec{s}=}6\mathbf{\vec{i}}-5\mathbf{\vec{k}}\] work done by the force is :

    A)  10 unit                                

    B)  \[122\sqrt{5}\] unit

    C)  \[5\sqrt{122}\] unit      

    D)         20 unit

    Correct Answer: A

    Solution :

    Work done\[=\overset{\to }{\mathop{\mathbf{F}}}\,\cdot \overset{\to }{\mathop{\mathbf{s}}}\,\] \[=(5\widehat{\mathbf{i}}+3\widehat{\mathbf{j}}+4\widehat{\mathbf{k}})\cdot (6\widehat{\mathbf{i}}-5\widehat{\mathbf{k}})\] \[=(5\widehat{\mathbf{i}}+3\widehat{\mathbf{j}}+4\widehat{\mathbf{k}})\cdot (6\widehat{\mathbf{i}}+0\widehat{\mathbf{j}}-5\widehat{\mathbf{k}})\] \[=(30+0-20)=10\,\,unit\]


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