'if diametre of earth is reduced to half mass remains constant what is then duration of day and night'
angular momentum remains the same.
I2 omega 2 = I1 omega 1
I = constant * m R^2
If m2 = m1
and
R2 = .5 R1
then
m R2^2 = .25 m R1^2
and I2 = (1/4) I1
(1/4)I1 omega2 = I1 omega1
omega2 = 4 omega1
T2 = (1/4) T1
day is 6 hours long instead of 24 so at the equator at equinox we have 3 hours dark and three hours light. :)
Come to think of it, anywhere at equinox you will have three hours light and three hours dark
To determine the duration of day and night if the diameter of the Earth is reduced to half while the mass remains constant, we need to consider the concept of angular momentum and its relationship with the rotation of the Earth.
To calculate the duration of day and night, we need to understand the concept of angular momentum. Angular momentum is the product of the moment of inertia and angular velocity. In simpler terms, it is the measure of an object's resistance to changes in its rotation.
When the diameter of the Earth is reduced to half, let's assume that the mass remains constant. This means that the moment of inertia of the Earth will decrease, as the moment of inertia is directly proportional to the square of the radius (or diameter).
Since the mass of the Earth remains constant, there will be no change in the gravitational force acting on it. Therefore, the torque acting on the Earth will still be the same.
According to the law of conservation of angular momentum, if no external torque acts on a rotating object, its angular momentum remains constant. In this case, the Earth experiences no external torque, so its angular momentum will remain the same.
If the moment of inertia decreases (due to the reduction in diameter) but the angular momentum remains constant, the angular velocity of the Earth must increase to compensate for the decrease in moment of inertia.
As the Earth's angular velocity increases, the Earth will complete one rotation faster. This means that the duration of the day (the time taken for one complete rotation) will decrease. The duration of the night will also decrease correspondingly.
To calculate the exact values, we will need specific data and performing mathematical calculations using the formulas of rotational motion. However, based on the given scenario, we can conclude that if the diameter of the Earth is halved while the mass remains constant, the duration of the day and night will decrease.