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