If the earth suddenly shrinks to 1 64 of its original volume, while keeping the same mass, then the duration of the day will be (Assume earth is a perfect sphere)

Step-by-step solution

If earth shrinks to 1 64 of its original volume; 4 3 r^3= 1 64 ( 4 3 R^3 ) Here, r= new radius and R= original radius aligned & r^3 & = R^3 64 or & r & = R 4 aligned As there is no external torque, angular momentum of earth remains constant i.e., I₁ ₁=I₂ ₂ [ I_ sphere = 2 5 M R^2 ] aligned & 2 5 M R^2 2 T₁ = 2 5 M r^2 2 T₂ & ( = 2 T , T= time of revolution about axis ) aligned T₂= r^2 T₁ R^2 T₂= R^2 16 T₁ R^2 [ r= R 4 ] array ll & T₂= T₁ 16 = 24 16 ~h or & T₂=1.5 ~h array