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

Answer

D

Explanation

`dw=vecF*vecdr=vecF*(dxhati+dyhatj)`
`=Kint (xdx)/((x^2+y^2)^(3//2))+(ydy)/((x^2+y^2)^(3//2))`
`x^2+y^2=a^2`
`w=k/a^3undersetaoverset0intxdx+underset0oversetaintydy=k/a^3(-a^2/2+a^2/2)=0`