If The Earth Suddenly Contract By One Fourth Of Its Present Radius By How Much Would The Day Be Shortened

if the earth suddenly contract by one fourth of its present radius , by how much would the day be shortened ?


Ok lets start the answer:-
Present Earth Mass :- M
       –            –      Radius:- R

Now, According to Question,
New Radius is R/4
And Earth Mass is same i.e. M

As we know
T=2π/√(GM/R³)                                     -(1)

Then, Present T is 24hours→86400seconds
R=[(43200)²*GM/π²]^1/3                  -(2)

Now, New T will be
T’=2π/√(GM/R’³)                         (where R’ is R/4)
On solving and putting values,
T’=43200 seconds
i.e., T’=12hours               [>>This is Answer<<]

Therefore, the answer is the day will be shortened by 12 hours as compared to real one!

I hope you like it!