AIIMS 2018 Physics Gravitational Potential Energy Assertion Reason Question

The assertion is true because the potential energy gained when an object of mass $m$ is raised to a height equal to the radius of the Earth $R$ is given by $U = mgh$, where $h = R$, resulting in $U = mgR$. However, the statement that this gain is $\frac{1}{2} mgR$ is false, as the correct expression does not include the factor of $\frac{1}{2}$. Therefore, while the assertion is true, the reasoning provided is incorrect, making option C the right choice. Options A and B are incorrect because they imply that the reasoning correctly explains the assertion, which it does not, and option D is incorrect as the assertion is indeed true.