Gravitation Question 122

Question:The gravitational field due to a mass distribution is $ [E=K/x^{3}] $ in the x-direction. (K is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance x is [MP PET 1994]

Options:

A) $ [K/x] $

B) $ [K/2x] $

C) $ [K/x^{2}] $

D) $ [K/2x^{2}] $

Show Answer

Answer:

Correct Answer: D

Solution:

Gravitational potential $ [=\int _{{}}^{{}}{I\ dx=\int _{x}^{\infty }{{}}\frac{K}{x^{3}}dx}] $ $ [=K,( \frac{x^{-3+1}}{-3+1} ) _{x}^{\infty }=| \frac{-K}{2x^{2}}| _{x}^{\infty }=\frac{K}{2x^{2}}] $



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