Question

The gravitational field in a region is given by:
$\overline{E}=\left(5N/kg\right)\hat{i}+\left(12N/kg\right)\hat{j}$
If the potential at the origin is taken to be zero the ratio of the potential at the points $(12m,0)$ and $(0,5m)$ is:

• A. zero
• B. $1$
• C. $144/25$
• D. $25/144$

Answer 1

The correct option is B $1$

Gravitational field in a region is given by

$E=\left(5N/kg\right)i+\left(12N/kg\right)j$

(Potential at origin is O)$\to$ given

and we know that $E=\frac{dv}{dr}=(dv=Edr)$

In vector from position vector

$=mi+oj=0\hat{i}+5\hat{j}d{V}_1=E.d{r}_1=(5\hat{i}+12\hat{j}).12\hat{i}+0\hat{j}=12\times 5d{V}_2=E.d{r}_2=(5\hat{i}+12\hat{j}).0\hat{i}+5\hat{j}=5\times 12\frac{d{V}_1}{d{V}_2}=1$