Question

The gravitational field in a region is given by $\overline{E}=(4\hat{i}+\hat{j})N/kg$. Work done by this field is zero when a particle is moved along the line.

• A. y+4x=2
• B. 4y+x=6
• C. x+y=5
• D. All of these

Answer 1

The correct option is A

y+4x=2

Work done will be zero when displacement is perpendicular to the field.

The field makes an angle

${\theta }_1=ta{n}^{-1}\left(\frac{1}{4}\right)$ with positive x-axis

While the line y + 4x = 2 makes and angle

${\theta }_2=ta{n}^{-1}(-4)$ with positive x-axis

$\therefore$ ${\theta }_1+{\theta }_2={90}^{\circ }$

i.e., the line y + 4x = 2 is perpendicular to $\overline{E}$.