Gravitational potential in a region is given | vedclass

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(A) The gravitational intensity $\vec{I}$ is related to the gravitational potential $V$ by the relation: $\vec{I} = -
abla V = -\left( \frac{\partial

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$(\hat{i} + \hat{j} + \hat{k})$

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(A) The gravitational intensity $\vec{I}$ is related to the gravitational potential $V$ by the relation: $\vec{I} = -
abla V = -\left( \frac{\partial V}{\partial x} \hat{i} + \frac{\partial V}{\partial y} \hat{j} + \frac{\partial V}{\partial z} \hat{k} ight)$.Given $V = -(x + y + z)$.Calculating the partial derivatives:$\frac{\partial V}{\partial x} = -1$,$\frac{\partial V}{\partial y} = -1$,and $\frac{\partial V}{\partial z} = -1$.Substituting these into the expression for $\vec{I}$:$\vec{I} = -[(-1)\hat{i} + (-1)\hat{j} + (-1)\hat{k}] = \hat{i} + \hat{j} + \hat{k} 	ext{ N/kg}$.Thus,the gravitational intensity at any point,including $(2, 2, 2)$,is $(\hat{i} + \hat{j} + \hat{k}) 	ext{ N/kg}$.

Gravitational potential in a region is given by $V = -(x + y + z) \text{ J/kg}$. Find the gravitational intensity at $(2, 2, 2)$ in $\text{N/kg}$.

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