InterviewSolution
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InterviewSolution
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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 isA. `(2 k pi)/(a)`B. `(k pi)/(a)`C. `(k pi)/(2a)`D. zero |
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Answer» Correct Answer - D `W = int vec F. d vec r` =`k underset(r_(A)) overset(r_(B))int[(x hat i)/((x^(2) +y^(2))^(3//2))+(y hat j)/((x^(2) +y^(2))^(3//2))](d xhat i+ dy hatj)` =`k underset(r_(A)) overset(r_(B))int (xdx)/((x^(2)+y^(2)))+(ydy)/((x^(2) +y^(2))^(3//2))` =`k underset(r_(A)) overset(r_(B)) int (1)/((x^(2)+y^(2))^(3//2))[d((x^(2))/(2))+d((y^(2))/(2))]` =`k underset(r_(A)) overset(r_(B)) int (1)/((x^(2)+y^(2))^(3//2)) (x^(2)+y^(2))` =`k underset(r_(A)) overset(r_(B)) int (1)/(2r^(3))d(r^(2)) = k underset(r_(A)) overset(r_(B)) int (2rdr)/(2r^(3)) = k underset(r_(A)) overset(r_(B)) int (dr)/(r^(2))` =`k[-(1)/(r)]_(r_(A))^(r_(B)) =k[(1)/(r_(A))-(1)/(r_(B))]` But `r_(A) =a `and `r_(B) =a` , `:. W = 0`. |
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