The Roche Limit tells us about the point on a rotating planet where the gravitational force at the equator is just equal to the necessary centripetal force needed for rotation.Assuming the planet to be a uniform sphere of density 5520 kg/m³,find the shortest period of rotation possible before exceeding the Roche Limit.(G = 6.67 $\times$ 10^-11 N·m²/kg²) A)none of the following B)50 mins C)150 mins D)48 mins E)85 mins

Question

Quizplus · Accepted Answer

The Roche limit concept is actually about the distance within which a celestial body, held together only by its own gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction. However, the question seems to misinterpret the Roche limit, focusing instead on a planet's rotation. To find the shortest period of rotation before reaching a critical limit (not the Roche limit as traditionally defined), we can use the formula for gravitational force and centripetal force equilibrium. Given the density and the gravitational constant, we can calculate the necessary period of rotation. The correct calculation involves equating gravitational force to centripetal force to find the period, which results in the period closest to 85 minutes from the given options.

The Roche Limit Tells Us About the Point on a Rotating