Question

The gravitational field in a region is given by $\overrightarrow{g}=[4\hat{i}+\hat{j}]Nk{g}^{-1}$. Work done by this field is zero when the particle moves along the line
(Choose the appropriate option)

• A. $y+4x=2$
• B. $4y+x=2$
• C. $x+y=5$
• D. All of the above

Answer 1

The correct option is A $y+4x=2$

Work done is zero when the displacement is perpendicular to the field.
The field makes, ${\theta }_1={\tan }^{-1}\left[\frac{1}{4}\right]$ with positive $X-$ axis.
While the line $y+4x=2$ makes the angle,
${\theta }_2={\tan }^{-1}[-4]$ with positive $X-$ axis.

As ${\theta }_1+{\theta }_2={90}^{\circ }$
i.e., the line $y+4x=2$ is perpendicular to $\overrightarrow{g}$