(B) The work done $W$ by a variable force $F$ is given by the integral of force with respect to displacement: $W = \int F \, dx$.Given the force $F =

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

$\frac{aL^2}{2} + \frac{bL^3}{3}$

(B) The work done $W$ by a variable force $F$ is given by the integral of force with respect to displacement: $W = \int F \, dx$.Given the force $F = ax + bx^2$,we integrate from the unstretched position $(x = 0)$ to the stretched position $(x = L)$:$W = \int_{0}^{L} (ax + bx^2) \, dx$$W = \left[ \frac{ax^2}{2} + \frac{bx^3}{3} \right]_{0}^{L}$Substituting the limits:$W = \left( \frac{aL^2}{2} + \frac{bL^3}{3} \right) - (0 + 0)$$W = \frac{aL^2}{2} + \frac{bL^3}{3}$

Class 11 Physics Work, Energy, Power and Collision Work Done by Variable Force and Force-Displacement Graph

Medium

When a rubber band is stretched by a distance $x$,it exerts a restoring force $F = ax + bx^2$,where $a$ and $b$ are constants. The work done in stretching the rubber band by a distance $L$ from its unstretched position is:

A
$\frac{1}{2}(aL^2 + bL^3)$
B
$\frac{aL^2}{2} + \frac{bL^3}{3}$
C
$\frac{aL^2}{3} + \frac{bL^3}{5}$
D
$\frac{aL^2}{7} + \frac{bL^3}{9}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Work, Energy, Power and Collision

Subtopic

Work Done by Variable Force and Force-Displacement Graph

$A$ $10 \, kg$ mass moves along the $x-$axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from $x = 0$ to $x = 8 \, cm$?

View Solution

What will be the area under the graph of variable force versus position?

Medium

View Solution

When a rubber band is stretched by a distance $x$,it exerts a restoring force of magnitude $F = ax + bx^2$,where $a$ and $b$ are constants. The work done in stretching the unstretched rubber band by $L$ is

MediumJEE MAIN 2014

View Solution

Obtain the equation of work done by a variable force in one dimension.

Medium

View Solution

An object of mass $500 \; g$, initially at rest, is acted upon by a variable force whose $X$-component varies with $X$ as shown in the graph. The velocities of the object at $X = 8 \; m$ and $X = 12 \; m$ are, respectively:

MediumNEET 2019

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

When a rubber band is stretched by a distance $x$,it exerts a restoring force $F = ax + bx^2$,where $a$ and $b$ are constants. The work done in stretching the rubber band by a distance $L$ from its unstretched position is:

Similar Questions

$A$ $10 \, kg$ mass moves along the $x-$axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from $x = 0$ to $x = 8 \, cm$?

What will be the area under the graph of variable force versus position?

When a rubber band is stretched by a distance $x$,it exerts a restoring force of magnitude $F = ax + bx^2$,where $a$ and $b$ are constants. The work done in stretching the unstretched rubber band by $L$ is

Obtain the equation of work done by a variable force in one dimension.

An object of mass $500 \; g$, initially at rest, is acted upon by a variable force whose $X$-component varies with $X$ as shown in the graph. The velocities of the object at $X = 8 \; m$ and $X = 12 \; m$ are, respectively:

Vedclass Test Series

Exam Paper Generator

Online Exam Module