Question

the gravitational field in a region is given by $E=(2\overrightarrow{i}+3\overrightarrow{j})Nk{g}^{-1}$ Show that no work is done by th egravitational field when a particle is moved on the line 3y + 2x = 5

Answer 1

$\overrightarrow{E}=2\hat{i}+3\hat{j}$
The field is represented as
$\tan {\theta }_1=\frac{3}{2}$

Again the line 3y + 2x
= 5 can be represented as
$\tan {\theta }_2=-\frac{2}{3}{m}_1{m}_2=-1$
Since the direction of field and the displacement are perpendicular, is done by the particle on the line.