Question

Gravitational potential at $x=2m$ is decreasing at a rate of $10J/kg-m$ along the positive x-direction. It implies that the magnitude of gravitational field at $x=2m$ is also $10N/kg$. Is this statement true or false?

Answer 1

$\left|\overrightarrow{E}\right|=\sqrt{{\left(-\frac{\partial V}{\partial x}\right)}^2+{\left(-\frac{\partial V}{\partial y}\right)}^2+{\left(\frac{-\partial V}{\partial z}\right)}^2}$
${\left(-\frac{\partial V}{\partial x}\right)}^2=10$J/kg-m is given
No information is given about
$-\frac{\partial V}{\partial y}$
and $-\frac{\partial V}{\partial z}$
So, $\left|\overrightarrow{E}\right|\ge 10$ N/kg