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Classical Mechanics
Level
pending
Assume earth's one fourth mass to be scooped out and placed in place of moon at the same distance, find how long a day would be?let mass of earth=81×mass of moon.
The answer is 217.329243.
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1 solution
Let earth-moon centre to centre distance be x,then the centre of mass(barycentre) of the system lies at a distance x/82 from earth's centre,balance the gravitational force and centrifugal force on earth about the barycentre,you will get the earth's orbital velocity,then find the time period,in the same way balance it for the new moon and earth ,you will find that the centre of mass of the new system lies at a distance x/4 from earth's centre then find the time period of earth about this centre of mass and compare it with the above time period the second one will be √(82) times the first one ie.24×√(82).