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If a particle is compelled to move on a given smooth plane curve under the action of given forces in the plane $\vec{F} = x \hat{i} + y \hat{j}$ , then:

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F→⋅dr→=xdx+ydy

∫F→⋅dr→≠12mv2

F→⋅dr→≠xdx×ydy

12mv2≠∫(xdx+ydy)

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detailed solution

Correct option is A

F→⋅dr→=(xi^+yj^)⋅(dxi^+dj^+dzj^)=xdx+ydy

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If a particle is compelled to move on a given smooth plane curve under the action of given forces in the plane F→=xi^+yj^, then:

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If a particle is compelled to move on a given smooth plane curve under the action of given forces in the plane $\vec{F} = x \hat{i} + y \hat{j}$ , then: