Question

A modified gravitational potential is given by \( V=-\frac{G M}{r}+\frac{A}{r^{2}} \). If the constant \( A \) is expressed in terms of gravitational constant (G), mass ( \( M \) ) and velocity of light (c), then from dimensional analysis, \( A \) is, (A) \( \frac{G^{2} M^{2}}{c^{2}} \)

Answer 1

Given, gravitational potential,

\(V=-\frac{GM}{r}+\frac{A}{r^2}\)

By principle of homogeneity,

According to the question,