If earth suddenly shrinks to 18th   of its original volume while mass remaining the same, then duration of day (in hour) will be

Original volume of the earth, V=43πR3Volume of earth after shrinkingV'=V4⇒  43πR3=18×43πR3R'=R2By conservation of angular momentum,I'ω'=Iω⇒  25MR2×2πT'=25MR2×2πT⇒  TT'=RR'2⇒  TT=RR/22⇒  TT'=4⇒  T'=T4=244      [∵T=24 h]=6 h