Question

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

• A. $71J$
• B. $13\surd \left(58\right)J$
• C. $-71j$
• D. $2j$

Answer 1

The correct option is D $2j$

Given: $\overrightarrow{g}=5iN/kg+12jN/kg$

Mass= 2kg

Solution: The gravitational field is given by,

$dV=-\overrightarrow{E}.\overrightarrow{dr}$

dV= -(5i +12j) (7i -3j) = -(35-36) = 1

So, change in gravitational potential energy is given by,

$dU=mdV$

$U=2\left(1\right)=2J$

Hence, the correct option is (D).