Question

If the radius of earth is contracted to half of the origional,the number of days of earth in one rotation around sun becomes???
please answer with explaination.Best answer will be rewarded with brainest
​

Answer 1

Hey mate!

Here's your answer

==================================

We can consider two scenarios: one with a constant mass and the other with change in mass proportional to the change in volume.

In both cases, the same principle applies: the conservation of angular momentum. Angular momentum is

L=I×ω

where I is the inertia moment and ω is the angular velocity. The angular momentum L is conserved, meaning it must stay the same value, so if the inertia I decreases by some factor, the speed ω has to increase by the same factor.

For a sphere (let’s assume the Earth is a perfect sphere): I=25mR2 ( m is the mass and R is the radius)

So let’s find out how I changes in both scenarios.

Scenario 1: constant mass

If the radius is halved, that means the inertia moment is reduced by a factor 4 (because of the R2 ). So the angular speed ω must be increased by a factor 4, which means a day would be 6 hours instead of 24.

Scenario 2: changing mass

if the mass changes proportionnally to the volume, it means the mass is reduced by a factor 8 (because the volume of a sphere is proportional to R3 ). So the inertia moment is reduced by a factor 4 because of the radius, and by a factor 8 because of the mass. So the total reduction is by a factor 32! which means the angular speed is increased by a factor 32, so a full day is only 45 minutes long.

=================================

If it helps then pls tell