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,   \[W={{W}_{1}}+{{W}_{2}}=0-k{{a}^{2}}=-k{{a}^{2}}\]

"> 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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A force \[\overset{\to }{\mathop{F}}\,=-k(y\hat{i}+x\hat{j})\] acts on a particle moving in the x -y plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the j'-axis to the point (a, a). The total work done by the force is

NEET Physics in NEET 10 months ago

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[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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