If the earth suddenly shrinks to 1 64 th of its original volume with its mass remaining the same, the period of rotation of earth becomes 24 x h . The value of x is ________

Step-by-step solution

L = constant; L = I ω From the conservation of angular momentum, 2 5 M R 2 ω 1 = 2 5 M R 4 2 ω 2 ⇒ M R 2 ω 1 = M R 2 ω 2 16 ⇒ ω 1 ω 2 = 1 16 Using ω = 2 π T for each case along with the respective angular frequencies, T 2 T 1 = 1 16 ⇒ T 1 T 2 = 16 1 Using T 1 = 24   h ,   x = 16 by comparing with the given time period in the question.