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NEET Sample Paper NEET Sample Test Paper-46

  • question_answer
    A body is displaced from \[\left( 0,\text{ }0 \right)\text{ }to\text{ }\left( 1\text{ }m,\text{ }1\text{ }m \right)\]along the path \[x\text{ }=\text{ }y\] by a force\[\overrightarrow{F}=\left( {{x}^{2}}\widehat{j}+\text{ }y \right)N\]. The work done by this force will be -

    A) \[\frac{4}{3}J\]

    B)                    \[\frac{5}{6}J\]

    C)                    \[\frac{3}{2}J\]

    D)                    \[\frac{7}{5}J\]

    Correct Answer: B

    Solution :

    \[W=\,\,\int\limits_{(0,\,\,0)}^{(1,\,\,1)}{\overrightarrow{F}.\overrightarrow{d}x}\] Here \[\overrightarrow{d}s\text{ }=\text{ }dx\widehat{i}+dy\widehat{j}\,\,+\,\,dz\,\widehat{k}\] \[\therefore \,\,\,\,W\,=\,\int\limits_{(0,\,\,0)}^{(1,\,\,1)}{({{x}^{2}}dy\,+\,ydx)}\] \[\,=\,\int\limits_{(0,\,\,0)}^{(1,\,\,1)}{({{x}^{2}}dy\,+\,x.dx)}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(as\,\,x\,\,=\,\,y)\] \[\therefore \,\,\,\,W\,\,=\,\,{{\left[ \frac{{{y}^{3}}}{2}+\frac{{{x}^{2}}}{2} \right]}^{(1,\,\,1)}}_{(0,\,\,0)}=\,\,\,\frac{5}{6}\,J\]


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