A position-dependent force F=7-2 x+3 x^2 N acts on a small body of mass 2 kg and displaces it f

Name: Problem 9, Chapter 4: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-10-05T14:09:32-08:00
Duration: 1 min 31 s
Channel: Dheeraj Sharma
Description: A position-dependent force F=7-2 x+3 x^2 N acts on a small body of mass 2 kg and displaces it from x=0 to x=5 m . The work done in joule is (A) 70 J (B) 270 J (C) 35 J (D) 135 J

step 1 In this question we have given a position dependent force that acts on a small body of mass 2 KG

Question

A position-dependent force $F=7-2 x+3 x^{2} N$ acts on a small body of mass $2 \mathrm{~kg}$ and displaces it from $x=0$ to $x=5 \mathrm{~m} .$ The work done in joule is (A) $70 \mathrm{~J}$ (B) $270 \mathrm{~J}$ (C) $35 \mathrm{~J}$ (D) $135 \mathrm{~J}$

   A position-dependent force $F=7-2 x+3 x^{2} N$ acts on a small body of mass $2 \mathrm{~kg}$ and displaces it from $x=0$ to $x=5 \mathrm{~m} .$ The work done in joule is
(A) $70 \mathrm{~J}$
(B) $270 \mathrm{~J}$
(C) $35 \mathrm{~J}$
(D) $135 \mathrm{~J}$

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 4, Problem 9

Instant Answer

Solved by Expert Dheeraj Sharma

10/05/2021

Step 1

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A position-dependent force $F=7-2 x+3 x^{2} N$ acts on a small body of mass $2 \mathrm{~kg}$ and displaces it from $x=0$ to $x=5 \mathrm{~m} .$ The work done in joule is (A) $70 \mathrm{~J}$ (B) $270 \mathrm{~J}$ (C) $35 \mathrm{~J}$ (D) $135 \mathrm{~J}$

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Key Concepts

Work Done by a Variable Force

This concept involves calculating the work performed when a force that varies with position acts on an object. The work is computed by integrating the force function over the displacement, which accumulates the infinitesimal contributions of work throughout the object's trajectory.

Definite Integral

The definite integral is a key concept in calculus used to compute the accumulation of a continuously varying quantity over a certain interval. In the context of work done by a force, it sums the infinitesimal products of the force and displacement over the path of motion.

Position-dependent Force

A position-dependent force is one whose magnitude and possible direction vary with the position of the object along its path. This variability necessitates the use of integration to accurately determine the total work done, as opposed to the simpler multiplication used for constant forces.

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