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BHU PMT BHU PMT Solved Paper-2001

  • question_answer
    A force \[\overset{\to }{\mathop{\text{F}}}\,=\left( 5\hat{i}+3\hat{j} \right)\,\,\text{N}\] is applied over a particle which displaces it from its original to the point\[\overset{\to }{\mathop{s}}\,=\left( 5\overset{\to }{\mathop{\text{i}}}\,+3\overset{\wedge }{\mathop{\text{j}}}\, \right)\,\,m\]. The work done on the particle is:

    A)  \[+11\,\,j\]                       

    B)   \[+7\,\,j\]

    C)  \[+13\,\,j\]                       

    D)  \[-7\,\,j\]

    Correct Answer: B

    Solution :

    Work (W) is measured by the product of the Applied force and the displacement of the body in The direction of the force (F) that is \[W=F\times \Delta s\] Where \[\Delta s\] is displacement Given, \[\overset{\to }{\mathop{F}}\,=5\overset{\wedge }{\mathop{i}}\,+3\overset{\wedge }{\mathop{j}}\,,\Delta s=\left( 2\overset{\wedge }{\mathop{i}}\,-\overset{\wedge }{\mathop{j}}\, \right)\] \[W=\left( 5\overset{\wedge }{\mathop{i}}\,+3\overset{\wedge }{\mathop{j}}\, \right).\left( 2\overset{\wedge }{\mathop{i}}\,-\overset{\wedge }{\mathop{j}}\, \right)\,\] \[W=10-3=7\,J\] Note: Both force and displacements are vector Quantities but work is a scalar quantity.


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