Question

The gravitational field in a region is given by $\vec{g} = 5N/kg \hat{i} + 12 N /kg \hat{j}.$ The change in the gravitational potential energy of a particle of mass $2\, kg$ when it is taken from the origin to a point ($7\, m$, $— 3\, m$) is :

• A. $71\, J$
• B. $13\sqrt{58}\,j$
• C. $-71\, J$
• D. $1\, J$

Answer 1

Answer: (D)

Gravitational field, $I = \left(5\hat{i}+12\hat{j}\right) N/kg$
$I = -\frac{dv}{dr}$
$v = -\left[\int\limits^{x}_{0} I_{x} dx+\int\limits^{x}_{0} I_{y} dy\right]$
$= -\left[I_{x}.X+I_{y}.Y\right]$
$= -\left[5 \left(7-0\right)+ 12 \left(-3-0\right)\right]$
$= -\left[35+ \left(-36\right)\right] = 1\, J/kg$
i.e., change in gravitational potential 1 J/kg.
Hence change in gravitational potential energy 1 J