Question

A particle free to move along $y-$ axis has potential energy
$U\left(y\right)=k[1-e^{-y^2}]$ for $-a\le y\le a$ where $k$ is a constant. Then

• A. At $y=0$, potential energy $=0$
• B. At $y=\pm a$, potential energy is maximum
• C. At $y=0$, kinetic energy is maximum
• D. At $y=\pm a$, Kinetic energy is minimum

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A At $y=0$, potential energy $=0$
B At $y=\pm a$, potential energy is maximum
C At $y=0$, kinetic energy is maximum
D At $y=\pm a$, Kinetic energy is minimum

$U\left(y\right)=k[1-e^{-y^2}]$ for $-a\le y\le a$
At $y=0,U\left(y\right)=0$
At $y=\pm a,U\left(y\right)\to {\text{max}}^m$
At $y=0$
K.E. $\to {\text{max}}^m$ because at $y=0$,
P.E. $={\text{min}}^m$
At $y\to \pm a\text{K.E.}\to {\text{min}}^m$, P.E $\to {\text{max}}^m$