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

Text Solution

Solution : Here, <br> final volume, `V_(2) = (1)/(64)` initial volume, `V_(1)` <br> i.e., `(4)/(3) pi R_(2)^(3) = (1)/(64) xx (4)/(3) pi R_(1)^(3)` <br> `R_(2)^(3) ((1)/(4) R_(1))^(3) or R_(2) = (1)/(4)R_(1)` <br> As no external torque is acting, <br> `L = I omega = I ((2pi)/(T)) = constant` <br> i.e., `I_(2)//T_(2) = I_(1)//T_(1)` <br> `((2)/(5) M R_(2)^(2)) (1)/(T_(2)) = ((2)/(5)M R_(1)^(2)) xx (1)/(T_(1))` <br> `T_(2) = (R_(2)^(2))/(R_(1)^(2)) xx T_(1)` <br> As `T_(1) =` time taken by earth to complate one revolution about its axis. <br> i.e., normal lenght of the day `= 24` hours <br> `:. T_(2) = ((1)/(4))^(2) xx 24 = 1.5h`