Question

A body is acted upon by a force that is inversely proportional to the displacement covered s. The work done will be proportional to:

• A. s
• B. s²
• C. $\sqrt{s}$
• D. none of the above

Answer 1

The correct option is D

none of the above

Step1: Given data

$F=\frac{a}{s}[F=force,a=cons\tan t,s=displacement]$

Step2: Work done

1. Work done is elaborated in such a way that it includes both forces exerted on the body and the total displacement of the body.
2. Work done is a scalar quantity.
3. It's S.I. unit is joules $(J)$.

Step3: Formula used

$dW=\overrightarrow{F}.\overrightarrow{ds}[W=workdone,F=force,s=displacement]$

Step3: Calculating work done

$$\begin{gathered} dW=\overrightarrow{F}.\overrightarrow{ds}=\frac{a}{x}dx \\ W=\int \frac{a}{x}dx=a\ln s \end{gathered}$$\

Since, the derived answer does not match any of the given options,

Hence, option D is the correct answer.