Question

Gravitational potential in a region is given by v=-(x+y+z) find the gravitational intensity at 2,2,2

Answer 1

we know formula , $V=-\vec{G}.\vec{dr}$
or , $G=-\frac{dV}{dr}$
where G is gravitational field intensity ,
V is gravitational potential,
and dr is position vector.

given, V = -(x + y + z)
we have to use partial derivatives concepts
so, $G_x=-\frac{\delta{(-x)}}{\delta{x}}\hat{i}$
$G_x=\hat{i}$

similarly, we can get,
$G_y=\hat{j}$
$G_z=\hat{k}$

now, $G=\hat{i}+\hat{j}+\hat{k}$