The work done on a particle of mass m by a force K x x 2 + y 2 3 / 2 i ^ + y x 2 + y 2 3 / 2 j ^ (K being a constant of appropriate dimensions, when the particle is taken from the point (a,0) to the point (0,a) along a circular path of radius a about the origin in the x-y plane is

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Aicharya · Accepted Answer

$dw = \vec{F} \cdot d\vec{r} = \vec{F} \cdot (dx\hat{i} + dy\hat{j}) = K \left( \int \frac{xdx}{(x^2 + y^2)^{3/2}} + \int \frac{ydy}{(x^2 + y^2)^{3/2}} \right)$ $x^2 + y^2 = a^2$ $w = \frac{K}{a^3} \left( \int_0^a xdx + \int_0^a ydy \right) = \frac{K}{a^3} \left( \frac{-a^2}{2}+ \frac{a^2}{2} \right) = 0$

The work done on a particle of mass m by a force K x x 2 + y 2 3 / 2 i ^ + y x 2 + y 2 3 / 2 j ^ (K being a…

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