Question

The work done by a force $\overrightarrow{F}=(-6x^3\hat{i})N$ is displacing a particle from $x=4m$ to $x=-2m$ is

• A. $-240J$
• B. $360J$
• C. $120J$
• D. $420J$

Answer 1

The correct option is B $360J$

$F=-6x^3\hat{i}$

$x=4$ to $x=-2$

$\int dw=\int f.dx$

As displacement is along $\hat{i}$ so $F=-6x^3$

$-\int {}_4^{-2}6x^{3}dx={\left[\frac{6x^4}{4}\right]}_4^{-2}$

${[\frac{-6x^4}{4}+\frac{6x^4}{4}]}_4^{-2}$

$\frac{-6\times {\left(4\right)}^4}{4}+\frac{60{(-2)}^4}{4}$

$=360J$