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) $ [71\ \text{J}] $
B) $ [13\sqrt{58}J] $
C) $ [-71\ \text{J}] $
D) $ [1\ \text{J}] $
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Answer:
Correct Answer: D
Solution:
- Gravitational field, $ [ \vec{g}=\left( 5\hat{i}+12\hat{j} \right)N/kg] $
$ [I=\frac{dQ}{dt}] $
$ [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]=1,J/kg]$
i.e., change in gravitational potential 1 J/kg. Hence change in gravitational potential energy is 1 J
BETA
