A) 192J
B) \[\frac{400}{3}J\]
C) \[\frac{287}{2}J\]
D) None of these
Correct Answer: C
Solution :
[c] From given graph: \[\vec{F}=\left( \frac{3}{4}x+10 \right)\hat{i}+\left( 20-\frac{4}{3}y \right)\hat{j}+\left( \frac{4}{3}z-16 \right)\hat{k}\] \[\operatorname{W}=\int{\vec{F}.\overrightarrow{ds}}\] \[=\int\limits_{\left( 0,5,6 \right)}^{\left( 2,10,0 \right)}{\left( \frac{3}{4}x+10 \right)\hat{i}+\left( 20-\frac{4}{3}y \right)\hat{j}+\left( \frac{4}{3}z-16 \right)\hat{k}}\] \[[dx\,\hat{i}+dy\,\hat{j}+dz\,\,\hat{k}]=\frac{287}{2}J\] Work done can also be found by finding area under these curves.
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