Question

The graph shown below represents the variation of the force as a function of position for a body.


Find out the work done by the force in moving the body from $x=3\text{m}$ to $x=7\text{m}$.

• A. $12\text{J}$
• B. $20\text{J}$
• C. $10\text{J}$
• D. $14\text{J}$

Answer 1

The correct option is A $12\text{J}$

Fundamental formula of workdone by a force (having constant direction) is:
$W=\int Fds$

hence, $W=$ area under the $\left(F\text{vs}S\right)$ graph.

Work done by force in moving the body from
$(x=3\text{m})$ to $(x=7\text{m})=$ will be area under the curve between $(x=3\text{m})$ to $(x=7\text{m})$
$\therefore W=(2\times 1)+(\frac{1}{2}\times (2+4)\times 2)+(4\times 1)$
$\therefore W=2+6+4=12\text{J}$