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Grade: 11
        
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.
one year ago

Answers : (1)

Arun
24510 Points
							
Dear student
 
Assume earth radius R
 
moment of inerta of earth
I1 = 2/5 MR^2
 

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

one year ago
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