Physics - Gravitation Question with Solution | TestHub

The asteroid Ceres is the smallest rocky body in the solar system having a spherical shape (smaller bodies have irregular shapes). Astronomical bodies can attain a spherical shape if the gravitational pressure at the center of the sphere equals or exceeds the ultimate volume stress of the material. If a spherical body rotates, it tends to become oblate. If the angular velocity of rotation is large enough to make the apparent value of $g$ at the equator (for the spherical shape) zero, then the body disintegrates. The equatorial radius $R_e$, the polar radius $R_p$, and the mean radius $R$ are related by the formula:

$$\frac{R_e-R_p}{R}=\frac{5{\omega }^2{R}^3}{4GM}$$

Here, $M$ is the mass of the rotating body.