The gravitational field in a region is given | vedclass

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(D) The gravitational field is given by $\vec{g} = (5\hat{i} + 12\hat{j})\,N/kg$.Since the field is uniform,the change in gravitational potential $\De

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$1$

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(D) The gravitational field is given by $\vec{g} = (5\hat{i} + 12\hat{j})\,N/kg$.Since the field is uniform,the change in gravitational potential $\Delta V$ is given by $\Delta V = -\int \vec{g} \cdot d\vec{r}$.For a displacement from $(0, 0)$ to $(7, -3)$,the change in potential is $\Delta V = -\vec{g} \cdot \Delta\vec{r}$.$\Delta\vec{r} = (7 - 0)\hat{i} + (-3 - 0)\hat{j} = 7\hat{i} - 3\hat{j}$.$\Delta V = -[(5\hat{i} + 12\hat{j}) \cdot (7\hat{i} - 3\hat{j})] = -[5(7) + 12(-3)] = -[35 - 36] = -(-1) = 1\,J/kg$.The change in gravitational potential energy $\Delta U = m \Delta V$.Given $m = 1\,kg$,$\Delta U = 1\,kg 	imes 1\,J/kg = 1\,J$.

The gravitational field in a region is given by $\vec{g} = 5\,N/kg\hat{i} + 12\,N/kg\hat{j}$. The change in the gravitational potential energy of a particle of mass $1\,kg$ when it is taken from the origin to a point $(7\,m, -3\,m)$ is ....... $J$.

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