Question

A particle moves in a potential region given by $U=8x^2-4x+400$. Its state of equilibrium will be

• A. $0.25M$
• B. $8M$
• C. $10M$
• D. $12M$

Answer 1

The correct option is A

$0.25M$

Step 1. Given Data,

$U=8x^2-4x+400$

Step 2. Formula Used,

Let the force be $F$.
${\displaystyle \frac{dU}{dx}}=F$

Step 3. Calculating the state of equilibrium,

Let the force be $F$,
${\displaystyle \frac{dU}{dx}}=F$
Differentiating the equation we get,
$$\begin{gathered} U=8x^2-4x+400 \\ \Rightarrow {\displaystyle \frac{dU}{dx}}=16x-4 \end{gathered}$$
Therefore, we get,
$F=16x-4$
In equilibrium condition,

$F=0$,
$16x-4=0$
$\therefore x=0.25m$
Therefore the state of equilibrium of the particle will be $0.25m$.

Hence, option A is the correct option.