What will be the duration of the day if the earth suddenly shrinks to of its original volume mass remain unchanged?

What will be the duration of the day if the earth suddenly shrinks to of its original volume mass remain unchanged?

Text Solution

Solution : Let `V_(1),V_(2)` are initial and final volume respectivelu. <br> `V_(2)=(1)/(27)V_(1)` <br> `(4)/(3) pir_92)^(3)=(!)/(27)(4)/(4) pir_(1)^(3)` <br> `pi r_(2)^(3)=(1)/(27)r_(1)^(3)` <br> `r_(2)=(1)/(3)r_(1)` <br> As there is no external force Threfore `L= Iomega` constant <br> `I_(1) omega_(1)=I_(2) omega_(2)` <br> `I_(1)(2pi)/(T_(1))=I_(2)((2pi)/(T_(2))` <br> `((2)/(5)Mr_(1)^(2))/((2)/(5)Mr_(2)^(2)))=(T_(1))/(T_(2))` <br> `rArr T_(2)=T_(1)((r_(2))/(r_(1)))^(2)` <br> As `T_(1)=24h`, <br> `T_(2)=24((1)/(3)(r_(1))/(r_(1)))^(2)=(24)/(9)=2.6h`