The work done on a particle of mass m by a force, $\ K[\frac{x}{(x^2 + y^2)^{3/2}}\hat{i} + \frac{y}{(x^2 + y^2)^{3/2}}\hat{j}]$

Q: The work done on a particle of mass m by a force, $\large K[\frac{x}{(x^2 + y^2)^{3/2}}\hat{i} + \frac{y}{(x^2 + y^2)^{3/2}}\hat{j}]$ (K being a constant 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

(a)(2 Kπ)/a

(b)( Kπ)/a

(c)( Kπ)/(2 a)

(d)0

Ans: (d)

Sol: Let P(x,y) be the point on circular path

Position vecrot $ \vec{r}=\vec{OP} = x \hat{i} + y \hat{j}$

$\vec{F} = \frac{K}{(x^2 + y^2)^{3/2}}(x \hat{i} + y \hat{j}) = \frac{K}{r^3}\vec{r}$

Since F is along radial direction , therefore work done is zero.