The earth rotates on its axis once a day. Suppose, by some process the earth contracts so that it's radius is only half as large as at present, then how long the earth will take to complete it's rotation?
Correct answer: C. 6 hours
- A. 24 hours
- B. 18 hours
- C. 6 hours
- D. 12 hours
Explanation
Here we assume that the mass of earth remains the same, moment of the inertia of the earth rotating about its axis is :I=⅖ MR^2-------eq1Angular velocity of the earth is:ω=2pi/T-------eq 2When the radius is reduced to half, The new moment of inertia isI=2/5MR^2=2/5M(R/2)^2----eq3New time period is T' an angular velocity is:ω'=2pi/T'Applying the law of conservation of angular momentum, we get:Iω=I'ω'From eq 1,2,3, and 4 we get(2/5MR^2)*(2pi/T)=[2/5M(R/2)^2]*(2pi/T')->T'=T/4But T=24 hrsT=24/6=6 hrs
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