Question

The potential energy of a particle of mass $1\text{kg}$ is, $U=10+(x-2{)}^2$. Here, $U$ is in $\text{joule}$ and $x$ in $\text{metre}$ on the positive $x-$axis. Particle travels upto $x=+6\text{m}$. Choose the correct statement.

• A. On negative $x-$axis particle travels upto $x=-2\text{m}$
• B. The maximum kinetic energy of the particle is $16\text{J}$
• C. Both $\left(a\right)$ and $\left(b\right)$ are correct
• D. Both $\left(a\right)$ and $\left(b\right)$ are wrong

Answer 1

The correct option is C Both $\left(a\right)$ and $\left(b\right)$ are correct

Given:
$U=10+(x-2{)}^2$

At extreme position, $x=6\text{m}$,

$U=10+(6-2{)}^2=26\text{J}$

On the other side

$U=26=10+(x-2{)}^2$

$x-2=\pm 4$

$\therefore x=6\text{m}or-2\text{m}$

Thus, $x=6\text{m}$ and $x=-2\text{m}$ are the extreme positions.

At $x=2\text{m}$, potential energy is minimum, which is $10\text{J}$.
Hence, at this position kinetic energy will be maximum, which is equal to total mechanical energy $(=26\text{J})$ minus minimum potential energy $(=10\text{J})$.
Thus, maximum kinetic energy is $16\text{J}$.