If the radius of earth contracts 1/n of its present day value, the length of the day will be approximately

Options

A. `(24)/(n)h`
B. `(24)/(n^(2))h`
C. `24 nh`
D. `24 n^(2)h`

Answer

B

Explanation

According to law of conservation of angular momentum, `Iomega` = constant
or `(R^(2))/(T)="constant"(as I prop R^(2) and omegaprop(1)/(T)and Iprop(1)/(omega))`
`:. T prop R^(2)`
As `R' = (1)/(n)R`
`(T)/(T')=((R)/(R'))^(2)rArr (T)/(T')=((Rxxn)/(R))^(2)`
`:. T'=(T)/(n^(2))=(24)/(n^(2))h`.