Question

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

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

Answer 1

The correct option is C Both (a) and (b) are correct

At $x=6m,U=26J$
On the other side
$U=26=10+(x-2{)}^2$
or $x-2=\pm 4$
$\therefore x=6m$
and $x=-2m$
Thus $x=+6m$ and $x=-2m$ are the extreme positions. At $x=2m$ , potential energy is minimum, which is $10J$. Hence, at this position kinetic energy will be maximum, which is equal to total mechanical energy $(=26J)$ minus minimum potential energy $(=10J)$. Thus maximum kinetic energy is $16J$