Question

A particle is moving on $x$ -axis has potential energy $U=2-20 x+5 x^{2}$ Joules along $x$ -axis. The particle is released at $x=3$. The maximum value of ' $x .$ ' will be:
$[x$ is in meters and $U$ is in joules]

• A. 5 m
• B. 3 m
• C. 7 m
• D. 8 m

Answer 1

Answer: (C)

$U=2-20 x+5 x^{2}$
$F=-\frac{d U}{d x}=20=10 x$
At equilibrium position; $F=0$
$ 20-10 x=0 $
$\Rightarrow x=2$
Since particle is released at $x=-3$, therefore amplitude of particle is 5 .

It will oscillate about $x=2$ with an amplitude of 5 .
$\therefore $ maximum value of $x$ will be 7