Question

By applying a force $\overrightarrow{F}=(3xy-5z)\}+4z\hat{k}$ a particle is moved along the path $y=x^2$ , where all quantitioare in SI units, from point $(0,0,0)$ m to the point $(2,4,0)$ m the work done by force $\overline{F}$ on theparticle (in joule), is

• A. $12J$
• B. $\frac{140}{5}$
• C. $\frac{232}{5}$
• D. $\frac{192}{5}$

Answer 1

The correct option is A $12J$

$\begin{array}{c}\overrightarrow{F}=\left(3xy-5z\right)\hat{i}+4z\hat{k}\\ w=\int F\left(dx\hat{i}+dy\hat{j}\right)\\ =\int 3xydx\\ ={\int }_0^{2}3x.\left(x^2\right)dx\\ =\frac{3}{4}{\left(x^{-1}\right)}_0^2\\ =\frac{3}{4}\times 16=12J\end{array}$

$\therefore$ Option $A$ is correct.