
Potential energy curve is shown in figure. Point at unstable equilibrium is:

(A) \[x = 6\]
(B) \[x = 4\]
(C) \[x = 2\]
(D) \[x = 3\]
Answer
149.4k+ views
Hint: An object is in equilibrium when the net force on it is zero. The force on a body can be given as the negative of the gradient of the potential energy. Unstable equilibrium occurs when a slight displacement will cause a decrease in potential energy.
Formula used: In this solution we will be using the following formulae;
\[F = - \dfrac{{dU}}{{dx}}\], where \[F\] is the force acting on a body, \[U\] is the potential energy of the body, and \[x\] is the position of the body.
\[\dfrac{{dU}}{{dx}}\] signifies an instantaneous rate of change of potential energy with distance (called gradient).
Complete Step-by-Step Solution:
A graph of potential energy with distance is given, and we are to find the point of unstable equilibrium.
Generally, we know that equilibrium exists where the sum of the forces acting on a body is zero. Hence we need first to identify the point of zero net force.
The force acting on a body can be given as
\[F = - \dfrac{{dU}}{{dx}}\], where \[F\] is the force acting on a body, \[U\] is the potential energy of the body, and \[x\] is the position of the body.
Hence, if \[F\] is zero, then \[\dfrac{{dU}}{{dx}} = 0\] i.e. the slope of the graph given is zero.
This occurs at a point where the tangent to the curve would be horizontal. And this occurs at point 2 and 6 in the curve given.
Now, the point of unstable equilibrium occurs at the maximum point of the curve (where the gradient is zero) which corresponds with point 2.
Hence, the correct option is C
Note: For clarity, unstable equilibrium corresponds to the maximum point because although the force at such point may be zero, any slight displacement will tend to reduce the potential energy of the body and hence the body continues to move (which is the description for unstable equilibrium). And generally, the potential energy of the body in any field whatsoever always tends towards the minimum.
Formula used: In this solution we will be using the following formulae;
\[F = - \dfrac{{dU}}{{dx}}\], where \[F\] is the force acting on a body, \[U\] is the potential energy of the body, and \[x\] is the position of the body.
\[\dfrac{{dU}}{{dx}}\] signifies an instantaneous rate of change of potential energy with distance (called gradient).
Complete Step-by-Step Solution:
A graph of potential energy with distance is given, and we are to find the point of unstable equilibrium.
Generally, we know that equilibrium exists where the sum of the forces acting on a body is zero. Hence we need first to identify the point of zero net force.
The force acting on a body can be given as
\[F = - \dfrac{{dU}}{{dx}}\], where \[F\] is the force acting on a body, \[U\] is the potential energy of the body, and \[x\] is the position of the body.
Hence, if \[F\] is zero, then \[\dfrac{{dU}}{{dx}} = 0\] i.e. the slope of the graph given is zero.
This occurs at a point where the tangent to the curve would be horizontal. And this occurs at point 2 and 6 in the curve given.
Now, the point of unstable equilibrium occurs at the maximum point of the curve (where the gradient is zero) which corresponds with point 2.
Hence, the correct option is C
Note: For clarity, unstable equilibrium corresponds to the maximum point because although the force at such point may be zero, any slight displacement will tend to reduce the potential energy of the body and hence the body continues to move (which is the description for unstable equilibrium). And generally, the potential energy of the body in any field whatsoever always tends towards the minimum.
Recently Updated Pages
JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Chemical Properties of Hydrogen - Important Concepts for JEE Exam Preparation

Trending doubts
Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Charging and Discharging of Capacitor

Ideal and Non-Ideal Solutions Raoult's Law - JEE

The time period of an artificial satellite in a circular class 11 physics JEE_Main

JEE Main Chemistry Question Paper with Answer Keys and Solutions

A pressure of 100 kPa causes a decrease in volume of class 11 physics JEE_Main

Other Pages
List of Fastest Century In IPL - Cricket League and FAQs

JEE Main Response Sheet 2025 Released – Download Links, and Check Latest Updates

JEE Main 2026 Syllabus PDF - Download Paper 1 and 2 Syllabus by NTA

NEET Physics Syllabus 2025 FREE PDF: Important Topics and Weightage

List of 10 Fastest Centuries in ODIs - Players and Countries

NCERT Solutions for Class 9 Maths Updated for 2024-25 Exam | Free PDF
