Question

The relationship between the force $F$ and position $x$ of a body is as shown in the figure. The work done in displacing the body from $x = 1\,m$ to $x = 5\,m$ will be

• A. 30 J
• B. 15 J
• C. 25 J
• D. 20 J

Answer 1

The Correct Option is D

$W =$ area under $F - x$ graph
From $X =0$ to $X =1$, force and displacement both are positive. Therefore work done is positive.
$
W _{0}=+\text { Area }=+5 J
$
From $X =1$ to $X =3$, force and displacement both are positive. Therefore work done is positive.
$
W _{1}=+\text { Area }=+15 J
$
From $X =3$ to $X =4$, force is negative but displacement is positive. Therefore work done is again positive.
$
\therefore W _{2}=-\text { Area }=-5 J
$
From $X =4$ to $X =5$, force and displacement both are positive. Therefore work done is again positive.
$
\therefore W _{3}=+\text { Area }=+5 J \\
W _{\text {Total }}= W _{0}+ W _{1}+ W _{2}+ W _{3}=20 J

$