Q111 / 200 · NEET 2022 (Phase 2) · Physics

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:

  • A
    $+\frac{K}{2}$
  • B
    $-\frac{\mathrm{K}}{2}$
  • Correct answer
    C
    $-\frac{\mathrm{K}}{4}$
  • D
    $+\frac{K}{4}$

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

Hence, the correct answer is option: 'C'.

More Gravitation Questions