Question

An object is displaced from point A(1, 2) to B(0, 1) by applying force $\overrightarrow{F}=x\hat{i}+2y\hat{j}$.
Find out work done(magnitude) by $\overrightarrow{F}$ to move the object from point A to B.

• A. 2 J
• B. 3.5 J
• C. 5 J
• D. 6.6 J

Answer 1

The correct option is B 3.5 J

$dW=\overrightarrow{F}.\overrightarrow{ds}$
$dW=(x\hat{i}+2y\hat{j})(dx\hat{i}+dy\hat{i})$
$dW={\int }_1^{0}xdx+{\int }_2^{1}2ydy$
$\therefore W=-3.5J$