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Which of the following is//are conservative force (s) ?A. `vec(F)=2 r^(3) hat(r)`B. `vec(F)= -(5)/(r)hat(r)`C. `vec(F)=(3(x hat(i)+y hat(j)))/((x^(2)+y^(2))^(3//2))`D. |
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Answer» Correct Answer - A::B::C Since , `W = int vec(F), vec(dr)` Clearly for forces (A) and (B) the integration do not require any information of the path taken. Force (C) : `W_(c) = int (3 (xhat(i) +y hatj))/((x^(2)+y^(2))^(3//2)) (dx hat(i)+dy hat(j))` `=3 int (x dx +y dy)/((x^(2)+y^(2))^(3//2))` Taking : `x_(2) + y_(2) =t` `2x dx + 2y dy = dt` `rArr xdx + ydy = (dt)/(2)` `rArr W_(c) = 3 int (dt//2)/(t^(3//2))=(3)/(2) int (dt)/(t^(3//2))` which is solvable. Hence (A), (B) and (C) are conservative forces But (D) requires some more information on path. Hence non-conservative. |
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