The work done by a force F→=-5x^4 i^ N in displacing a body from x=2 m to x=-2 m is

Correct answer: (C) 64 J. Work donedW=F.→dr→ ⇒dW=-5x^4 i^.dx i^ ⇒ dW=-5x^4dx ⇒ W=∫dW=∫2-2-5x^4dx ⇒ W= -x^5 2-2=64 J

Q128 / 160 · AP EAMCET 2019 (21 Apr Shift 2) · Physics

The work done by a force $\vec{F} = - 5 x^{4} \hat{i} N$ in displacing a body from $x = 2 m$ to $x = - 2 m$ is

Work done $(d W) = \vec{F .} d \vec{r}$

$\Rightarrow d W = (- 5 x^{4}) \hat{i} . (d x) \hat{i}$

$\Rightarrow d W = - 5 x^{4} d x$

$\Rightarrow W = \int d W = \int_{2}^{- 2} - 5 x^{4} d x$

$\Rightarrow W = {|\begin{matrix} - x^{5} \end{matrix}|}_{2}^{- 2} = 64 J$

Hence, the correct answer is option: 'C'.