if earth were suddenly shrink to half of its present radius without change in mass,what is the effect on duration of days?

When radius of the earth becomes half of the present radius, Angular momentum of the earth remains same to conserve the angular momentum.
Initial angular momentum = final Angular momentum

 = I'ω'where I is the moment of inertia of the earth at the present radius Rω is the angular frequency of rotation at the present radius R.I' is the moment of the inertia and ω' is the angular frequency when radius becomes half.When mass of the earth is constant , moment of inertia is directly proportional to the R2.ω = 2πT where T is the timer period of the earth which is equal to 24 hours.Let T' be the time period of the earth when radius becomes half.acc. to law of conservation of the angular momentum , we getR22πT = R'22πT'R' = R/2we get,T' = T4T' = 24/4 = 6 hours.

Hence new duration of the earth is 6 hours.


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