Physics - W.E.P. Question with Solution | TestHub

$$U^{\prime }=12x^2-10x=0\Rightarrow x=0,\frac{5}{6};U^{\prime \prime }=24x-10$$

At x = 0, $U^{\prime \prime }=-10<0$ - unstable (A wrong). At $x=5/6$, $U^{\prime \prime }=10>0$ - stable (B wrong).

(C) With KE = 1 J at the stable point, total energy $E=U(5/6)+1\approx -0.16<0=U(0)$, so the particle stays trapped in the well and oscillates - correct.

(D) $F(1)=-(12-10)=-2\mathrm{N}\Rightarrow |a|=2m/{\mathrm{s}}^2$ - correct.

Ans. (C,D)