Question

Given below is the plot of a potential energy function $U\left(X\right)$ for a system, in which a particle is in one dimenstional motion, while a conservative force $F\left(X\right)$ acts on it. Suppose that $E_{mech}=8\text{J}$, the incorrect statement for this system is :

• A. at $X>X_4$, K.E. is constant throughout the region.
• B. at $X<X_1$, K.E. is smallest and the particle is moving at the slowest speed.
• C. at $X=X_2$, K.E. is greatest and the particle is moving at the fastest speed.
• D. at $X=X_3$, K.E $=4\text{J}.$

Answer 1

The correct option is B at $X<X_1$, K.E. is smallest and the particle is moving at the slowest speed.


We have from the given diagram
$E_{mech}=8\text{J}$
(A) at $X>X_4$, $U=\text{constant}=6\text{J}$
$K.E=E_{mech}-U=2\text{J}=\text{constant}$

(B) at $X<X_1$, $U=\text{constant}=8\text{J}$
$K.E=E_{mech}-U=8-8=0\text{J}$
Particle is at rest.

(C) At $X=X_2$ $U=0\Rightarrow E_{mech}=K.E=8\text{J}$
$K.E$ is greatest, and particle is moving at fastest speed.

(D) At $(X=X_3)$,$U=\text{constant}=4\text{J}$
$K.E=E_{mech}-U=(8-4)\text{J}=4\text{J}$
Hence, option (b) is correct.