Dr. Who has discovered that the Daleks have devised a plot to destroy the univer

Question

Dr. Who has discovered that the Daleks have devised a plot to destroy the universe by shrinking it until it becomes infinitesimal. with the help of K-9, the Doctor computes that the Dalek's universe shrink machine smartphone app will shrink the universe at a rate that is inversely proportional to the geometric mean of the volume of the universe and time. If one-second after the shrink machine app is switched on, volume of the universe is 45.7 billion light years and the rate of shrinkage at that instant is equal to -2.3389013x10^-19 light years per second, how much time in minutes does it take before it shrinks to half its current volume.

Explanation / Answer

Volume of Universe=45.7 billion light years

radius of universe=(3*V/4*pi)^(1/3)

=2.21 billion light years

Volume when it is shrinked to half of its billion=45.7/2=22.85 billion light years

r=(3*V/4*pi)^(1/3)

=1.76 billion light years

Now change in radius=2.21-1.76=0.45 billion light years

therefore time taken

t=(0.45 light years)/(2.3389013x10^-19 light years per second)

=1.92*10^18 s

=3.2*10^16 min ans

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