Question

The graphs in $\mathbf{Fig}\mathbf{.}\mathbf{7}\mathbf{-}\mathbf{18}$ give the x-component ${\mathit{f}}_{\mathbf{x}}$of force acting on a particle moving along an x-axis. Rank them according to the work done by the force on the particle from $\mathit{x}\mathit{=}\mathit{0}$to $\mathit{x}\mathit{=}{\mathit{x}}_{\mathit{1}}$, from most positive work first to most negative work last.

Short answer

The rank of the graphs of the work done from most positive to most negative is $\left(\mathrm{b}\right)>\left(\mathrm{a}\right)>\left(\mathrm{c}\right)>\left(\mathrm{d}\right)$.

Step-by-step solution

The given data

The four graphs of the x-component of the force versus the displacement are given.

Understanding the concept of the work done

To rank work done, we have to find the area under the force versus displacement graph. Work done is a product of force and displacement. If force is a variable force, then work done is equal to the area under the force-displacement curve.

Calculation of the ranks of the graphs according to the work done

For Graph (a):

In this graph, the area under the curve before the intersection is the same as the area under the curve after the intersection. It means positive work done is exactly equal to the negative work done.

So, the work done is zero.

For Graph (b):

In this graph, the area under the curve before the intersection is greater than the area under the curve after the intersection.

It means positive work done is greater than negative work done.

So, work done is positive.

For Graph (c):

In this graph, the area under the curve before the intersection is less than the area under the curve after the intersection.

It means negative work done is greater than positive work done.

So, the work done is negative.

For Graph (d):

In this graph, the area under the curve before the intersection is greater than the area under the curve after the intersection.

It means negative work done is greater than positive work done.

So, this is the most negative work done.

Hence, the required rank of the graphs is $\left(\mathrm{b}\right)>\left(\mathrm{a}\right)>\left(\mathrm{c}\right)>\left(\mathrm{d}\right)$.