Answer

Verified

417.3k+ views

**Hint:**We are given a particle that experiences a variable force F=2x. The work is done in displacing the body from x = $x_1$ to x = $x_2$. This work done can be found by integrating the force F with respect to x, from x = $x_1$ to x = $x_2$. Here, the force is a function of x, so we’ll assume it is acting along the x-axis.

**Formula used:**

$W = \int\limits_{{x_2}}^{{x_1}} {Fdx} $

**Complete step-by-step answer:**

In the question, they’ve given a particle that is moving under the influence of force, F = 2x. Initially, the particle’s position is given by x = $x_1$ and the final position is given by x = $x_2$.

The work done by any force in displacing a body is given by

$W = \int {Fdx} $

Where,

W is the work done

F is the force acting on the particle

As the position is changing from $x_1$ to $x_2$, we can integrate it from its initial position to the final position. The work done will be given by

$W = \int\limits_{{x_2}}^{{x_1}} {Fdx} $

Substituting, F = 2x in the formula, we have

$\eqalign{

& W = \int\limits_{{x_2}}^{{x_1}} {Fdx} \cr

& \Rightarrow W = \int\limits_{{x_2}}^{{x_1}} {2xdx} \cr

& \Rightarrow W = 2\int\limits_{{x_2}}^{{x_1}} {xdx} \cr

& \Rightarrow W = 2\left| {\dfrac{{{x^2}}}{2}} \right|_{{x_2}}^{{x_1}} \cr

& \Rightarrow W = 2 \times \dfrac{{{x_2}^2 - {x_1}^2}}{2} \cr

& \Rightarrow W = {x_2}^2 - {x_1}^2 \cr} $

Therefore, the work done in moving the particle is ${x_2}^2 - {x_1}^2$.

**So, the correct answer is “Option B”.**

**Note:**Work done is actually the integral of the dot product of force and displacement. The dot product is the product of magnitudes and the cosine of the angle between them. In the question, we have not considered the dot product as the force and the displacement are in the same direction. Thus, the angle between them is zero and the cosine of zero is 1.

Recently Updated Pages

Which of the following is correct regarding the Indian class 10 social science CBSE

Who was the first sultan of delhi to issue regular class 10 social science CBSE

The Nagarjuna Sagar project was constructed on the class 10 social science CBSE

Which one of the following countries is the largest class 10 social science CBSE

What is Biosphere class 10 social science CBSE

Read the following statement and choose the best possible class 10 social science CBSE

Trending doubts

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Difference Between Plant Cell and Animal Cell

10 examples of law on inertia in our daily life