Question

If the earth were to suddenly contract to 1/nth of its present radius without any change in its mass the duration of the new day will be nearly

Answer 1

The new duration of the day will be 24/n² hrs

Explanation :

we know that the moment of inertia (I) is directly proportional to the square of the radius.

I ∝ r²

since the radius will become 1/n times, hence the moment of inertia will become 1/n² time

Hence

I₁ = I/n²

=> I/I₁ = n²

Now we know that the angular momentum is constant,

=> I₁ω₁ = Iω

=> ω₁ = ω(I/I₁)

= ωn²

Hence the angular velocity will increase by n² time.

we know that

T = 2π/ω

=> T ∝ 1/ω

hence when ω will increase by n² time time period will decrease by n² time

current time period = 24 hrs

So the new duration of the day will be 24/n² hrs

Answer 2

Answer:

24/n^2

Explanation:

Hope it helps u:)