A particle is acted upon by a conservative force F=(7 î-6 ĵ) N. The work done by the force when

Name: Problem 25, Chapter 4: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-10-06T13:36:55-08:00
Duration: 1 min 43 s
Channel: Dheeraj Sharma
Description: A particle is acted upon by a conservative force F=(7 î-6 ĵ) N. The work done by the force when the particle moves from origin (0,0) to the position (-3 m, 4 m ) is given by (A) 3 J (B) 10 J (C) -45 J (D) None of these

step 1 In this question we have given a particle and we have given the force that is acting on this par

Question

A particle is acted upon by a conservative force $F=(7 \hat{i}-6 \hat{j}) \mathrm{N}$. The work done by the force when the particle moves from origin $(0,0)$ to the position $(-3 \mathrm{~m}$, $4 \mathrm{~m}$ ) is given by (A) $3 \mathrm{~J}$ (B) $10 \mathrm{~J}$ (C) $-45 \mathrm{~J}$ (D) None of these

   A particle is acted upon by a conservative force $F=(7 \hat{i}-6 \hat{j}) \mathrm{N}$. The work done by the force when the particle moves from origin $(0,0)$ to the position $(-3 \mathrm{~m}$, $4 \mathrm{~m}$ ) is given by
(A) $3 \mathrm{~J}$
(B) $10 \mathrm{~J}$
(C) $-45 \mathrm{~J}$
(D) None of these

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 4, Problem 25

Instant Answer

Solved by Expert Dheeraj Sharma

10/06/2021

Step 1

We need to find the work done by this force when the particle moves from the origin to (-3, 4). The force is a conservative force given by $F=(7 \hat{i}-6 \hat{j}) \mathrm{N}$. The initial position of the particle is $R_1 = (0,0)$ and the final position is $R_2 = Show more…

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A particle is acted upon by a conservative force $F=(7 \hat{i}-6 \hat{j}) \mathrm{N}$. The work done by the force when the particle moves from origin $(0,0)$ to the position $(-3 \mathrm{~m}$, $4 \mathrm{~m}$ ) is given by (A) $3 \mathrm{~J}$ (B) $10 \mathrm{~J}$ (C) $-45 \mathrm{~J}$ (D) None of these

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Key Concepts

Work Done

Work is defined as the energy transferred by a force acting upon an object over a distance. In mechanics, it is computed by taking the dot product of the force vector and the displacement vector, which yields a scalar quantity representing the net energy transfer.

Dot Product

The dot product is a mathematical operation that multiplies two vectors, yielding a scalar. It incorporates the magnitudes of the vectors and the cosine of the angle between them, making it particularly useful for calculating work, as it effectively considers only the component of the force that acts in the direction of displacement.

Conservative Forces

A conservative force is one where the work done in moving an object between two points is independent of the path taken. This key concept allows the use of potential energy functions and simplifies energy calculations because only the start and end positions are important, not the journey between them.

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