Given below is the plot of a potential energy function U(x) for a… - Vidyadip

MCQ

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

A
at $x=x_{3}$, $K.E.=4\;J$
B
at $x=x_{2}$, $K.E.$ is greatest and the particle is moving at the fastest speed.
✓
at $x\,<\,x_{1}$, $K.E.$ is smallest and the particle is moving at the slowed speed.
D
at $x\,>\,x_{4}$, $K.E.$ is constant throughout the region.

✓

Answer

Correct option: C.

at $x\,<\,x_{1}$, $K.E.$ is smallest and the particle is moving at the slowed speed.

c
Given

$\left.E_{\text {mech. }}=8\right]$

$(A)$ at $x\,>\,x_{4}, \quad U=$ constant $\left.=6\right]$

${K}={E}_{{mech} .}-{U}=2\, {J}=$ constant

$(B)$ at $x\,<\,x_{1}, \quad U=$ constant $\left.=8\right]$

${K}={E}_{\text {mech. }}-{U}=8-8=0 \,{J}$

Particle is at rest.

$(C)$ At $x=x_{2}, U=0 \Rightarrow E_{\text {mech. }}=K=8$ ]

${KE}$ is greatest, and particle is moving at fastest speed.

$(C)$ $(D)$ At $\left.x=x_{3}, \quad U=4\right]$

${U}+{K} =8\, {J}$

${K} =4\, {J}$

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