Question

A body is displaced from $(0,0)$ to $(1m,1m)$ along the path $x=y$ by a force $F=\left(x^2\hat{j}+y\hat{i}\right)N$. The work done by this force will be :

• A. $\frac{4}{3}J$
• B. $\frac{5}{6}J$
• C. $\frac{3}{2}J$
• D. $\frac{7}{5}J$

Answer 1

The correct option is B $\frac{5}{6}J$

Along the path $x=y;\overrightarrow{F}=(x^2\hat{j}+y\hat{i})N$

$\Rightarrow \overrightarrow{F}(y^2\hat{j}+x\hat{i})N$ (as $x=y$)

we know;

Work done $=\int \overrightarrow{F}.d\overrightarrow{r}=\int F_{x}dx+\int F_{y}dy$

$={\int }_0^{1}xdx+{\int }_0^1{y}^{2}dy$

$={\left[\frac{x^2}{2}\right]}_0^1+{\left[\frac{y^3}{3}\right]}_0^1$

work done $=\frac{1}{2}+\frac{1}{3}=\frac{5}{6}J$

hence $Work=\frac{5}{6}J$ so $\left(B\right)$ option is correct