1. Tardigrade
  2. Question
  3. Physics
  4. The work done on a particle of mass m by a force K [( x /( x 2+ y 2)3 / 2) hat i +( y /( x 2+ y 2)3 / 2) hat j ] ( K being a constant of appropriate dimensions, when the particle is taken from the point ( a , 0) to the point (0, a ) along a circular path of radius a about the origin in the x-y plane is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The work done on a particle of mass $m$ by a force $K \left[\frac{ x }{\left( x ^{2}+ y ^{2}\right)^{3 / 2}} \hat{ i }+\frac{ y }{\left( x ^{2}+ y ^{2}\right)^{3 / 2}} \hat{ j }\right]$ ( $K$ being a constant of appropriate dimensions, when the particle is taken from the point $( a , 0)$ to the point $(0, a )$ along a circular path of radius a about the origin in the $x-y$ plane is

JEE AdvancedJEE Advanced 2013Work, Energy and Power

Solution:

$d w =\vec{ F } \cdot d \vec{ r }=\vec{ F } \cdot( d x \hat{ i }+ d \hat{ j }) $
$= K \int \frac{ x dx }{\left( x ^{2}+ y ^{2}\right)^{3 / 2}}+\frac{ ydy }{\left( x ^{2}+ y ^{2}\right)^{3 / 2}}$
$x ^{2}+ y ^{2}= a ^{2}$
$w =\frac{ K }{ a ^{3}} \int\limits_{ a }^{0} x d x +\int\limits_{0}^{ a } ydy $
$=\frac{ K }{ a ^{3}}\left(\frac{- a ^{2}}{2}+\frac{ a ^{2}}{2}\right)=0$