Question

A particle is moving on $x$ -axis has potential energy $U=\left(2 - 20 x + 5 x^{2}\right)$ 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. $5m$
• B. $3m$
• C. $7m$
• D. $8m$

Answer 1

Answer: (C)

$U=2-20x+5x^{2}$
$F=-\frac{d u}{d x}=20-10x\left[\right.F \propto -x\Rightarrow SHM\left]\right.$
At equilibrium $F=0$
$20-10x=0$
$x=2$ [mean position]
since particle is released at $x=-3,$ therefore
amplitude of particle is $5$