In a gravitational field, the gravitational potential is given by,…
In a gravitational field, the gravitational potential is given by, $\mathrm{V}=\frac{\mathrm{K}}{x}(\mathrm{~J} / \mathrm{kg})$. The gravitational field intensity at point $(2,0,3) \mathrm{m}$ is:
$+\frac{K}{2}$
$-\frac{\mathrm{K}}{2}$
$-\frac{\mathrm{K}}{4}$
$+\frac{K}{4}$
Solution
Gravitational field intensity \(=\frac{-\partial V}{\partial x} \hat{i}+\frac{-\partial V}{\partial y} \hat{j}+\frac{-\partial V}{\partial x} \widehat{k}\)
where V is gravitational potential
\(\Rightarrow\) Gravitational field intensity \(=\frac{-\partial}{\partial x}\left[\frac{-K}{x}\right]=\frac{-K}{x^2} \hat{i}\)
at \((2,0,3)\)
\(\overrightarrow{E_G}=\frac{-K}{2^2}=\frac{-K}{4} \hat{i}\)