What will be the duration of day and night if Earth shrinks to half the present radius?

Explanation

Reasoning:The duration of a day (the time it takes Earth to rotate once on its axis) is related to its angular momentum. Angular momentum is a conserved quantity, meaning it stays constant in the absence of external forces.Mathematically, angular momentum (L) is given by: L = I * ω, where:I is the moment of inertia of the rotating object (Earth)ω is the angular velocity (the rate of rotation)Impact of Shrinking Radius:If Earth shrinks to half its present radius, its moment of inertia (I) will decrease significantly**. This is because the moment of inertia depends on the mass distribution and the distance of mass elements from the axis of rotation. As the radius decreases, the average distance of mass elements from the axis also decreases, leading to a lower moment of inertia.To maintain the same angular momentum (L) despite the decrease in I, the angular velocity (ω) must increase.Effect on Day Length:Since angular velocity (ω) is directly related to the rotational period (T) (time taken for one rotation) through the equation: T = 2π / ω, increasing the ω will decrease the T.Therefore, when the Earth shrinks to half its radius, its rotational period will become shorter. The new day length (T) will be:T_new = (2π / ω_new) = (2π / ω_old) * (I_old / I_new)Since the moment of inertia decreases significantly (I_new < I_old), the new rotational period (T_new) will be significantly shorter than the original period (T_old). In this case, the new day length would be approximately 6 hours.