A) \[71\text{ }J\]
B) \[13\sqrt{58}J\]
C) \[-71\text{ }J\]
D) \[1\text{ }J\]
Correct Answer: D
Solution :
[d] Gravitational field, \[I=\left( 5\hat{i}+12\hat{j} \right)\text{ }N/kg\] \[I=\frac{dv}{dr}\] \[v=-\left[ \int\limits_{0}^{x}{{{I}_{x}}dx+\int\limits_{0}^{y}{{{I}_{y}}dy}} \right]=-[{{I}_{x}}.x+{{I}_{y}}.y]\] \[=-\left[ 5\left( 7-0 \right)+12\left( -3-0 \right) \right]\] \[=-\left[ 35+\left( -36 \right) \right]=1\operatorname{J}/kg\] i.e., change in gravitational potential 1 J/kg. Hence change in gravitational potential energy 1J
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