Question

if the earth were to suddenly contect to half its present seize,without any change in its mass,the duration of the new day will be

Answer 1

HI,

Considering the Earth a solid sphere, it's moment of inertia would be I= (2/5)MR^2

First Scenario(mass remains the same)

Now if mass remains the same, new moment of inertia will be I'=I/4

And according to law of conservation of angular momentum (Iw=I'w').

w'=4w

Also w=2π/T and w'=2π/T'

T'=T/4

T=24 hours

T'=24/4= 6 hours

Hence a day would be one- fourth of current duration

Second Scenario(mass changes according to volume)

if density of the Earth remains same then

mass=M, volume=V, density=d

M=V*d

V=(4/3)πR^3

V’=new volume

V’=V/8

M’=M/8

I=(2/5)MR^2

I’=(2/5)M’R’^2

I’=I/32

I’w’=Iw

w’=32w

w'=2π/T'

w’T’=wT

T’=T/32

T’=24/32=45 minutes

Although this is only theoretical assumption, in practical many more changes have to be faced from nature

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