Given below is a graph between a variable force (F) (along y -axis) and the displacement (X) (al

Name: Problem 445, Chapter 4: JEE Physics
Uploaded: 2021-10-04T11:14:43-08:00
Duration: 2 min 10 s
Channel: Narendra Kumar
Description: Given below is a graph between a variable force (F) (along y -axis) and the displacement (X) (along x -axis) of a particle in one dimension. The work done by the force in the displacement interval between 0 m and 30 m is (A) 275 J (B) 325 J (C) 400 J (D) 300 J

step 1 Here we have given a graph between a variable force F along Y axis and the displacement along X

Question

Given below is a graph between a variable force (F) (along $\mathrm{y}$ -axis) and the displacement $(\mathrm{X})$ (along $\mathrm{x}$ -axis) of a particle in one dimension. The work done by the force in the displacement interval between $0 \mathrm{~m}$ and $30 \mathrm{~m}$ is (A) $275 \mathrm{~J}$ (B) $325 \mathrm{~J}$ (C) $400 \mathrm{~J}$ (D) $300 \mathrm{~J}$

   Given below is a graph between a variable force (F) (along $\mathrm{y}$ -axis) and the displacement $(\mathrm{X})$ (along $\mathrm{x}$ -axis) of a particle in one dimension. The work done by the force in the displacement interval between $0 \mathrm{~m}$ and $30 \mathrm{~m}$ is
(A) $275 \mathrm{~J}$
(B) $325 \mathrm{~J}$
(C) $400 \mathrm{~J}$
(D) $300 \mathrm{~J}$

JEE Physics

StemEZ 1st Edition

Chapter 4, Problem 445

Instant Answer

Solved by Expert Narendra Kumar

10/04/2021

Step 1

In this case, the graph is divided into four sections: two triangles and two rectangles. Show more…

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Given below is a graph between a variable force (F) (along $\mathrm{y}$ -axis) and the displacement $(\mathrm{X})$ (along $\mathrm{x}$ -axis) of a particle in one dimension. The work done by the force in the displacement interval between $0 \mathrm{~m}$ and $30 \mathrm{~m}$ is (A) $275 \mathrm{~J}$ (B) $325 \mathrm{~J}$ (C) $400 \mathrm{~J}$ (D) $300 \mathrm{~J}$

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Key Concepts

Work

Work is a form of energy transfer that occurs when a force is applied over a displacement. The key formula for calculating work is the integral of force with respect to displacement, which allows for the determination of work even when the force is not constant.

Variable Force and Integration

When dealing with a force that varies with displacement, the calculation of work requires the use of integration. The work done is computed as the definite integral of the force function over the given limits of displacement, which effectively sums the contributions of variable force through the displacement.

Area Under a Curve

In the context of physics, particularly when finding work done by a variable force, the area under a force-displacement graph is equivalent to the integral of the force over displacement. This geometric interpretation of the integral provides a visual method for estimating or calculating the work done.

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