Question

if the earth suddenly contract to half of its radius without any change in its mass and shape ,duration of the day instead of 24 hours will be :
24 hour
12 hour
6 hour
8 hour​

Answer 1

Answer:

Since angular momentum of the earth remains constant,

Inertia (I) is proportional to Radius (R2).

As the radius of the earth is reduced to half of its original size, then Inertia I will decrease to (R2)2, which means 4 times the original inertia.

Therefore, the Angular Velocity will increase 4 times, as it inversely depends on the inertia.

As angular velocity increases 4 times, the time taken will be ¼th of the present time, due to much faster rotation.

Thus, the duration of the day will be 24 / 4 = 6 hours.

Answer 2

The duration will be 6 hours

Correct answer:- Option C ( 6 Hours )

Explanation:-

In this, The angular momentum of the earth will be stable/costant. And, In this I will be proportional to the Radius of the earth.

I = Inertia

According to the question, radius of the earth is reduced to half of its original size. It maans that, Earth radius is reduced in its 4 parts.

Therefore, The time taken for the earth will be 1/4th of the Earth's 24 hours.

Duratuon of earth = 24/4

= 6 Hours

Therefore, The duration of the day will be 6 hours.

Additional information:-

The radius of the earth is reduced by 4 times. So, the inertia (I) will be decreased to (R2) 2.

Which is = R × 2 × 2

Radius = 4 times reduced

So, 24/4 = 6 Hours