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The work done an a particle of mass m by...

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

A

`(2Kpi)/a`

B

`(Kpi)/a`

C

`(Kpi)/(2a)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
`W = int vec(F) .dvec(r ) = int vec(F) . (dxhat(i) +dxhat(j))`
`=K int (xdx)/((x^(2)+y^(2))^(3/2)) +(ydy)/((x^(2)+y^(2))^(3/2))`
Particle is moving on a circle with equation : `x^(2)+y^(2)=a^(2)`
`rArr " " W = K/(a^(3)) [int_(a)^(0)xdx +int_(0)^(a) ydy] = K/(a^(3))((-a^(2))/2 +(a^(2))/2)=0`
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