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`