First slide

Concept of potential energy

Question

The potential energy of a conservative system is given by $U= (10 x^{2} - 4 X) J$ .The equilibrium position is

Moderate

A

0.4m
B

0.2 m
C

0.1m
D

0.5m

Solution

$\begin{array}{l} U = 10 x^{2} - 4 x \\ F = \frac{- d v}{d x} = \frac{- d}{d x} (10 x^{2} - 4 x) \\ F = - [10 \times 2 x - 4] = 4 - 20 x \end{array}$
For equilibrium position
$\begin{array}{l} F = 0 \\ 4 - 20 x = 0 \Rightarrow 20 x = 4 \\ x = 0.2 m \end{array}$

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