(B) For a conservative force,$F = -\frac{dU}{dx} = -(2ax - b) = -2ax + b$. At the equilibrium position,$F = 0$,so $-2ax + b = 0$,which gives $x = \fra

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

$\frac{b}{2a}, -\frac{b^2}{4a}$

(B) For a conservative force,$F = -\frac{dU}{dx} = -(2ax - b) = -2ax + b$. At the equilibrium position,$F = 0$,so $-2ax + b = 0$,which gives $x = \frac{b}{2a}$. The equilibrium potential energy is $U = a(\frac{b}{2a})^2 - b(\frac{b}{2a}) = \frac{b^2}{4a} - \frac{b^2}{2a} = -\frac{b^2}{4a}$.

Class 11 Physics Work, Energy and Power Potential Energy

Medium

For a system of conservative forces,the potential energy is given by the formula $U = ax^2 - bx$,where $a$ and $b$ are constants. The equilibrium position and the equilibrium potential energy will be,respectively:

A
$\frac{b}{2a}, -\frac{b}{2a}$
B
$\frac{b}{2a}, -\frac{b^2}{4a}$
C
$\frac{b^2}{2a}, -\frac{b^2}{2a}$
D
$-\frac{b}{4a}, -\frac{b}{4a}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Work, Energy and Power

Subtopic

Potential Energy

If the potential energy between two molecules is given by $U = -\frac{A}{r^6} + \frac{B}{r^{12}}$,then at equilibrium,the separation between the molecules and the potential energy are:

DifficultJEE MAIN 2020

View Solution

If the potential energy of a particle is given by $U = A - Bx^2$,then the force is proportional to which of the following?

Medium

View Solution

In the equation $W = -mgh$,what does the negative sign indicate?

Medium

View Solution

$A$ number of identical cubical blocks of edge $a$ and mass $m$ are lying on a horizontal table. The work done on the blocks in arranging them in a column of height $(n + 1)a$ on the table is

Difficult

View Solution

$A$ uniform chain of length $2\,m$ is kept on a table such that a length of $60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain onto the table? (Take $g = 10\,m/s^2$) ................ $J$

DifficultAIEEE 2004

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

For a system of conservative forces,the potential energy is given by the formula $U = ax^2 - bx$,where $a$ and $b$ are constants. The equilibrium position and the equilibrium potential energy will be,respectively:

Similar Questions

If the potential energy between two molecules is given by $U = -\frac{A}{r^6} + \frac{B}{r^{12}}$,then at equilibrium,the separation between the molecules and the potential energy are:

If the potential energy of a particle is given by $U = A - Bx^2$,then the force is proportional to which of the following?

In the equation $W = -mgh$,what does the negative sign indicate?

$A$ number of identical cubical blocks of edge $a$ and mass $m$ are lying on a horizontal table. The work done on the blocks in arranging them in a column of height $(n + 1)a$ on the table is

$A$ uniform chain of length $2\,m$ is kept on a table such that a length of $60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain onto the table? (Take $g = 10\,m/s^2$) ................ $J$

Vedclass Test Series

Exam Paper Generator

Online Exam Module