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Gravitation question

2022 · Q171
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Gravitation question

2022 · Q171

NEETPhysicsGravitationMCQ+4 / −1

In a gravitational field, the gravitational potential is given by, V=−KxV = - {K \over x}V=−xK​ (J/Kg). The gravitational field intensity at point (2, 0, 3) m is

  1. A
    +K4+ {K \over 4}+4K​
  2. B
    +K2+ {K \over 2}+2K​
  3. C
    −K2- {K \over 2}−2K​
  4. D
    −K4- {K \over 4}−4K​
View written solutionFree

Correct answer: D

Gravitational field intensity $$ = {{ - \partial V} \over {\partial x}}\widehat i + {{ - \partial V} \over {\partial y}}\widehat j + {{ - \partial V} \over {\partial x}}\widehat k$$

where V is gravitational potential

$\Rightarrow$ Gravitational field intensity $$ = {{ - \partial } \over {\partial x}}\left[ {{{ - K} \over x}} \right] = {{ - K} \over {{x^2}}}\widehat i$$

at (2, 0, 3)

$$\overrightarrow {{E_G}} = {{ - K} \over {{2^2}}} = {{ - K} \over 4}\widehat i$$

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