Question

A force $F$ acting on a particle varies with the position $x$ as shown in figure. The work done by this force in displacing the particle from $x=-2m$ to $x=0$.

• A. $+10\text{J}$
• B. $+20\text{J}$
• C. $-20\text{J}$
• D. $-10\text{J}$

Answer 1

The correct option is D $-10\text{J}$

While moving $x=-2\text{m}$ to $x=0$, the particle has a positive displacement but the force acting on the particle is along negative $x$ direction.
$\therefore$ Work done by the force is negative.
Hence we can write for workdone by force as,
$W=-\left[\text{Area under}(F-x)\text{graph}\right]$
$\therefore W=-\left[\frac{1}{2}\right(2\left)\right(10\left)\right]=-10\text{J}$