A) \[-2k{{a}^{2}}\]
B) \[2\,\,k{{a}^{2}}\]
C) \[-k{{a}^{2}}\]
D) \[k{{a}^{2}}\]
Correct Answer: C
Solution :
| [c] \[{{W}_{1}}\int_{0}^{a}{\overset{\to }{\mathop{F}}\,.\overset{\to }{\mathop{dx}}\,}=\int_{0}^{a}{-k(y\hat{i}-x\hat{j}).\hat{i}dx}\] |
| \[=\int_{0}^{a}{-k(0\hat{i}}+x\hat{j}).\hat{i}dx=zero\] |
| \[W\int_{0}^{a}{\overset{\to }{\mathop{F}}\,.\overset{\to }{\mathop{dy}}\,}=\int_{0}^{a}{-k(y\hat{i}}+x\hat{j}).\hat{j}dy\] |
| \[=\int_{0}^{a}{-k(a\hat{i}}+a\hat{j}).\hat{j}dy\] |
| \[=-ka\int_{0}^{a}{dy=-k{{a}^{2}}}\] |
| Total work done, |
| \[W={{W}_{1}}+{{W}_{2}}=0-k{{a}^{2}}=-k{{a}^{2}}\] |
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