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AMU Medical AMU Solved Paper-2011

  • question_answer
    A particle is moved from a position \[{{r}_{1}}-\text{i}=\left( \text{3}\overset{\hat{\ }}{\mathop{\text{i}}}\,\text{ }+\text{ 2}\overset{\hat{\ }}{\mathop{\text{j}}}\,-\text{6k} \right)\]metre to a position \[{{r}_{2}}(14\overset{\hat{\ }}{\mathop{i}}\,+13\overset{\hat{\ }}{\mathop{j}}\,+9\overset{\hat{\ }}{\mathop{k}}\,)\]metre under the action of a force \[\text{F}=\left( \text{4}\overset{\hat{\ }}{\mathop{\text{i}}}\,+\overset{\hat{\ }}{\mathop{\text{j}}}\,+\text{3}\overset{\hat{\ }}{\mathop{\text{k}}}\, \right)\text{N}.\]The work done is equal to

    A)  32 J                                       

    B)  64 J

    C)  96 J                                       

    D)  100 J

    Correct Answer: D

    Solution :

                     Distance covered by particle                                 \[r={{r}_{2}}-{{r}_{1}}\]                                 \[=(14\hat{i}+13\hat{j}+9\hat{k})-(3\hat{i}+2\hat{j}-6\hat{k})\]                                 \[=11\hat{i}+11\hat{j}+15\hat{k}\]                 Work done, W = F . r                 \[=(4\hat{i}+\hat{j}+3\hat{k})\,\,(11\hat{i}+11\hat{j}+15\hat{k})\]                 = 44 + 11 + 45                 = 100 J


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