Question

A force $F$ acting on a particle varies with position $x$ as shown in figure. The workdone by this force in displacing the particle from $x=-1\text{m}$ to $1\text{m}$.

• A. $+20\text{J}$
• B. $0\text{J}$
• C. $-20\text{J}$
• D. $+10\text{J}$

Answer 1

The correct option is B $0\text{J}$

While moving from $x=-1\text{m}$ to $x=0\text{m}$, the particle has a positive displacement, but the force acting on the particle is along $-x$ direction.
From $x=0$ to $x=1\text{m}$,both displacement and force are along $+x$ direction.
$\therefore$ Work done $\left(W\right)=$ Area under $F-x$ graph = Area of tringle ODC - Area of tringle ABO
$=\frac{1}{2}(1-0)\times 5-\frac{1}{2}\times (0-(-1\left)\right)\times 5=\frac{5}{2}-\frac{5}{2}=0\text{J}$