Question

The gravitational field in a region is given by $\overrightarrow{E}=\left(4\hat{i}+\hat{j}\right)N/kg$. Workdone 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. None of these

Answer 1

The correct option is B $4y+x=6$

$\overrightarrow{E}=(\overrightarrow{4i}+\overrightarrow{j})N/kg$

$\overrightarrow{F}=m\overrightarrow{E}=(\overrightarrow{4i}+\overrightarrow{j})N$

$4y+x=6$

$y=\frac{6-x}{4}$

when $x_1=0,y_1=\frac{3}{2}$

when $x_2=6,y_2=0$

$\overrightarrow{d}=(x_2-x_1)\hat{i}+(y_2-y_1)\hat{j}=3\hat{i}+\frac{3}{2}\hat{j}$

$W=\overrightarrow{F}\times \overrightarrow{d}=(\overrightarrow{4i}+\overrightarrow{j})\times (3\hat{i}+\frac{3}{2}\hat{j})=0$

$\overrightarrow{F}\perp \overrightarrow{d}$