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 Kx)/(a)`
B. `(Kx)/(a)`
C. `(Kx)/(2a)`
D. `0`

Answer

D

Explanation

`dW = vecF cdot vecd r = vecF cdot (d x hati + dt hatj) " " K int(xdx)/((x^2 + y^2)^(3//2)) + (ydy)/((x^2 + y^2)^(3//2))`
`x^2 + y^2 = a^2 " "W = k/(a^3) int_a^0 xdx + int_0^a ydy = k/(a^3) ((-a^2)/(2) + (a^2)/2) = 0`