Question

The relationship between the force F and position x of a body is as shown in 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. $20J$

Answer 1

The correct option is D $20J$

Word done $=\overrightarrow{f}\cdot \overrightarrow{ds}=$ area under force displacement curve

$W=\overrightarrow{f}\cdot \overrightarrow{ds}$

Here work done is area under curve from $x=1m$ to $x=5m$

$W=\frac{1}{2}(1+2)\left(10\right)+(1\times 5)-(1\times 5)+(\frac{1}{2}\times 1\times 10)=15+5-5+5=20J$