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NEET 2022
Exam
NEET
Year
2022
Subject
Physics
Chapter
Gravitation

NEET 2022 · Physics · Gravitation

In a gravitational field, the gravitational potential is given by,...

In a gravitational field, the gravitational potential is given by, V=Kx( J/kg)\mathrm{V}=\frac{\mathrm{K}}{x}(\mathrm{~J} / \mathrm{kg}). The gravitational field intensity at point (2,0,3)m(2,0,3) \mathrm{m} is:

Options

  1. A+K2+\frac{K}{2}
  2. B−K2-\frac{\mathrm{K}}{2}
  3. C−K4-\frac{\mathrm{K}}{4}
  4. D+K4+\frac{K}{4}

Correct answer

C. −K4-\frac{\mathrm{K}}{4}

Step-by-step 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)(2,0,3) (\overrightarrow{E_G}=\frac{-K}{2^2}=\frac{-K}{4} \hat{i})
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