Question

A force $\overrightarrow{F}=x\hat{i}+2y\hat{j}$ is applied on a particle. Find out work done by $F$ to move the particle from point $A$ to $B$

• A. $-3.5J$
• B. $-2.5J$
• C. $-4.5J$
• D. $-4J$

Answer 1

The correct option is A $-3.5J$

It is given that,

$F=x\hat{i}+2y\hat{j}$

$Let,dx=dx\hat{i}+dy\hat{j}$

$dw=\int F.dx$

$=\int (x\hat{i}+2y\hat{j}\left)\right(dx\hat{i}+dy\hat{j})$

$=\underset{1}{\overset{0}{\int }}xdx+2\underset{2}{\overset{1}{\int }}ydy$

$={{\frac{x^2}{2}|}_1}^0+{{y^2|}_2}^1$

$=\frac{-1}{2}+(1-4)$

$=-0.5-3$

$=-3.5J$