Question

The work done on a particle of mass m by a force k\([\frac{x}{(x^2+y^2)^{\frac{1}{2}}}i+\frac{y}{(x^2+y^2)^{\frac{1}{2}}}j]\) (k being a constant of appropriate dimensions), when the particle is taken from a point (a, 0) to a point (0, a) along a circular path of radius ‘a’ about the origin in the x–y plane is

(1) 2Kπ/a

(2) kπ/a

(3) kπ/2a

(4) 0

Answer 1

(4) 0

In the figure; 

r = xi + yj

∴ F is along r or the force is radial and the particle is moved along the circular path

∴ F ⟂ S

∴ Work done = zero