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

Options

A. `(2 K pi)/(a)`
B. `(K pi)/(a)`
C. `( K pi)/(2a)`
D. `0`

Answer

D

Explanation

Let us consider a point on the circle . The equation of is `vecF = K[ ( xhati)/((x^(2) + y^(2) ) ^(3//2)) + (Yhatj)/((x^(2) + y^(2) ) ^(3//2))] `
`vecF = K[ (x i)/((a^(2))^(3//2)) + (Yj)/((a^(2) (3//2))]`
`barF = (K)/(a^(3) [x I +Y j]`

The force acts redialy outwards as shown in the figure and the displacement is tengential to the circular . Therefore the angle between the force and displacement is `90^(@)` and `W= 0`
option (d) is correct .