Question:
The gravitational field in a region is given by: \(\vec{E} = (5\ N/kg)\hat{i} + (12\ N/kg)\hat{j}\). If the potential at the origin is taken to be zero, then the ratio of the potential at the points \((12\ \mathrm{m}, 0)\) and \((0, 5\ \mathrm{m})\) is :
The gravitational field in a region is given by: \(\vec{E} = (5\ N/kg)\hat{i} + (12\ N/kg)\hat{j}\). If the potential at the origin is taken to be zero, then the ratio of the potential at the points \((12\ \mathrm{m}, 0)\) and \((0, 5\ \mathrm{m})\) is :
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For a uniform field, \(V = -\vec{E}\cdot\vec{r}\) with \(V(0)=0\).
Updated On: Nov 4, 2026
- Zero
- 1
- \(\frac{144}{25}\)
- \(\frac{25}{144}\)
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The Correct Option is B
Solution and Explanation
\(E_x = -\dfrac{\partial V}{\partial x} = 5\) and \(E_y = -\dfrac{\partial V}{\partial y} = 12\), so \(V = -(5x + 12y)\) (with \(V(0,0)=0\)).
At \((12, 0)\): \(V_1 = -(5\times 12) = -60\ \mathrm{J/kg}\).
At \((0, 5)\): \(V_2 = -(12\times 5) = -60\ \mathrm{J/kg}\).
Ratio \(V_1 : V_2 = 1\).
Answer: (2) 1
At \((12, 0)\): \(V_1 = -(5\times 12) = -60\ \mathrm{J/kg}\).
At \((0, 5)\): \(V_2 = -(12\times 5) = -60\ \mathrm{J/kg}\).
Ratio \(V_1 : V_2 = 1\).
Answer: (2) 1
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