A) -7 J
B) Zero
C) +7 J
D) d) +19 J
Correct Answer: C
Solution :
Given, the two-dimensional force \[F=3{{x}^{2}}\hat{i}+4\hat{j}\] \[\vec{r}=x\hat{i}+y\,\hat{j}\] \[d\,\vec{r}=dx\,\hat{i}+dy\,\hat{j}\] Kinetic energy = Work done \[W=\int{F.\,\,d\,\vec{r}}\] \[=\int_{\,(2,3)}^{\,(3,0)}{(3{{x}^{2}}\hat{i}+4\,\hat{j})}.\,(dx\,\hat{i}+dy\,\hat{i})\] \[=\int_{\,(2,3)}^{\,(3,0)}{(3{{x}^{2}}}dx+4dy\,\] \[=\int_{\,(2,3)}^{\,(3,0)}{3{{x}^{2}}}dx+\int_{3}^{0}{4dy\,}\] \[=[{{x}^{3}}]_{2}^{3}+4[y]_{3}^{0}\] \[=(27-8)+4(-3)\] \[=19-12=7J\]You need to login to perform this action.
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