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If the earth , supposed to be a uniform sphere , contracts slightly so that its radius decreases by 1/n times than the present radius , show that the duration of the day decreases by 48/n hours.
Dear student Assume earth radius R moment of inerta of earthI1 = 2/5 MR^2 Now according to questionEarth radius becomes R – R/n MI of the earth of radius(R/n) I2 = 2/5 (R – R/n)^2 There is no external torque on the earth So, Angular momentum would be conserveI1 w1 = I2 w2 you will get T = 24 (1 + 2/n)^-1 T = 24 (1 – 2/n) hence day is shorten by 24 – 24 (1 – 2/n) = 48/n
Now according to question
Earth radius becomes R – R/n
MI of the earth of radius
(R/n)
I2 = 2/5 (R – R/n)^2
There is no external torque on the earth
So, Angular momentum would be conserve
I1 w1 = I2 w2
you will get
T = 24 (1 + 2/n)^-1
T = 24 (1 – 2/n)
hence day is shorten by
24 – 24 (1 – 2/n) = 48/n
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