Gravitation Question 364
Question: The gravitational field in a region is given by$ [\vec{g} =5N/kg\hat{i}+12N/kg\hat{j}] $ . The change in the gravitational potential energy of a particle of mass 1 kg when it is taken from the origin to a point $ [(7m,-3m)] $ is:
Options:
A) $ [71J] $
B) $ [13\sqrt{58}J] $
C) $ [-71J] $
D) $ [1J] $
Show Answer
Answer:
Correct Answer: D
Solution:
-
Gravitational field, $ [I=\left( 5\hat{i}+12\hat{j} \right)N/kg] $
$ [I=\frac{dv}{dr}] $
$ [v=-\left[ \int\limits_{0}^{x}{I_{x}dx+\int\limits_{0}^{y}{I_{y}dy}} \right]=-[I_{x}.x+I_{y}.y]] $
$ [=-\left[ 5\left( 7-0 \right)+12\left( -3-0 \right) \right]] $
$ [=-\left[ 35+\left( -36 \right) \right]=1J/kg] $
i.e., change in gravitational potential 1 J/kg. Hence change in gravitational potential energy 1J
