Question

If radius of earth suddenly contracts to th of its
present radius without any change in its mass, the
duration of day will approximately become
24
24
(1) 24 hour
(2) 24 hour
(3) 24 n hour
(4) 24n2 hour​

Answer 1

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

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