Question

If $F=2 x^{2}-3 x-2$, then select the correct statement

• A. $x=-\frac{1}{2}$ is the position of stable equilibrium
• B. $x=2$ is the position of stable equilibrium
• C. $x=-\frac{1}{2}$ is the position of unstable equilibrium
• D. $x=2$ is the position of neutral equilibrium

Answer 1

Answer: (A)

$F=2 x^{2}-3 x-2$
Putting $F=0$
$2 x^{2}-3 x-2=0$
$2 x^{2}-4 x+x-2=0$
$2 x(x-2)+(x-2)=0$
$(x-2)(2 x+1)=0$
$\Rightarrow x=2,\,\, x=\frac{-1}{2}$
$\frac{d^{2} v}{d x^{2}}=\frac{-d F}{d x}=-(4 x-3)$
at $x=\frac{-1}{2}$
$\frac{d^{2} v}{d x^{2}} > 0$
$\Rightarrow $ Stable equilibrium