JEE Advanced 2024 Physics question on Gravitation

A particle of mass $m$ is under the influence of the gravitational field of a body of mass $M$ ($\gg m$). The particle is moving in a circular orbit of radius $r_0$ with time period $T_0$ around the mass $M$. Then, the particle is subjected to an additional central force, corresponding to the potential energy $V_c(r) = m\alpha/r^3$, where $\alpha$ is a positive constant of suitable dimensions and $r$ is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius $r_0$ in the combined gravitational potential due to $M$ and $V_c(r)$, but with a new time period $T_1$, then $(T_1^2 - T_0^2)/T_1^2$ is given by

[$G$ is the gravitational constant.]