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Potential energy function along `x-`axis in a certain force field is given as `U(x)=(x^(4))/(4)-2x^(2)+(11)/(2)x^(2)-6x` For the given force field `:-` (i)the points of equilibrium are `x=1`, `x=2` and `x=3` (ii) the point `x=2` is a point of unstable equilibrium. (iii) the points `x=1` and `x=3` are points of stable equilibrium. (iv) there exists no point of neutral equilibrium. The correct option is `:-`A. `(i),(ii),(iv)`B. `(i),(ii),(iii),(iv)`C. (iii),(iv)D. (ii),(iii) |
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Answer» Correct Answer - B For equilibrium points, `F=-(dU)/(dx)=0rArrx^(3)-6x^(2)+11x-6=0rArrx=` `1,x=2` and `x=3` In stable equilibrium , `(d^(2)U)/(dx)gt0rArrx=1` and `x=3` are stable while `x=2` is unstable. In neutral equilibrium, `(dU)/(dx)=0` and `(d^(2)U)/(dx)=0` |
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