Question

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

Answer: (B)

As force is a function of $r$ , therefore
$W=\displaystyle \int _{\left(0,0\right)}^{\left(1,1\right)} \overset{ \rightarrow }{F} . \overset{ \rightarrow }{d} x$
Here $d\overset{ \rightarrow }{s}=dx\hat{i}+dy\hat{j}+dz\hat{k}$
$\therefore $ $W=\displaystyle \int _{\left(0,0\right)}^{\left(1,1\right)}\left(x^{2} d y + y d x\right)=\displaystyle \int _{\left(0,0\right)}^{\left(1,1\right)}\left(y^{2} d y + x d x\right)$ (as $x=y$ )
$\therefore $ $W=\left(\left[\frac{y^{3}}{3} + \frac{x^{2}}{2}\right]\right)_{\left(0,0\right)}^{\left(1,1\right)}=\frac{5}{6}J$