Question

Differentiate between stable and unstable equilibrium.

Answer 1

Hint
We can clearly observe from the problem statement that this is a question for the straight approach. In this question we just have to mention the basic characteristics, example, basic difference and some properties and we get the sufficient points for the answer.

Complete step by step Solution
Stable Equilibrium:
The mathematical equation for the Stable Equilibrium is: $\dfrac{{{d^2}U}}{{d{x^2}}} > 0$
In this when we displace any object from its equilibrium it will get back to its normal position. This shows the negative slope on phase point of equilibrium.
Eg. The coming back of the ball to its original position in the center in a hemispherical bowl.
Unstable Equilibrium:
The mathematical equation for the Stable Equilibrium is: $\dfrac{{{d^2}U}}{{d{x^2}}} < 0$
In this when we displace any object from its equilibrium it will get further away and not get back to its normal position. This shows the positive slope on phase point of equilibrium.
Eg. Rolling of the ball down from the slope of a hill.

Note
In these types of questions we just have to be elaborative and precise at the same time so that we can conclude all the points. We just have to take care of keeping the definition along with an example necessarily in these kinds of questions.