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AMU Medical AMU Solved Paper-2006

  • question_answer
    A  particle   moves   with   a   velocity \[\left( \text{5}\overset{\hat{\ }}{\mathop{\text{i}}}\,-\text{3}\overset{\hat{\ }}{\mathop{\text{j}}}\,\text{ }+\text{ 6}\overset{\hat{\ }}{\mathop{\text{k}}}\, \right)\text{ m}/\text{s}\]under the influence of a constant force \[\overset{\to }{\mathop{\text{F}}}\,=\text{1}0\overset{\hat{\ }}{\mathop{\text{i}}}\,+\text{1}0\overset{\hat{\ }}{\mathop{\text{j}}}\,+\text{2}0\overset{\hat{\ }}{\mathop{\text{k}}}\,\text{ N}.\] The instantaneous power applied to the particle is

    A)  200 J/s                                

    B)  40 J/s

    C)  140 J/s                                

    D)  170 J/s

    Correct Answer: C

    Solution :

                     \[\vec{v}=(5\hat{i}-3\hat{j}+6\hat{k})\,m/s\] \[\vec{F}=(10\hat{i}+10\hat{j}+20\hat{k})\,N\] \[\therefore \]  Power \[\vec{P}=\vec{F}.\,\vec{v}\]                 \[=(10\,\hat{i}+10\hat{j}+20\hat{k})\,.\,(5\hat{i}-3\hat{j}+6\hat{k})\]                 - 50 - 30 + 120                 = 250 J/s


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