### 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 ?**

###### Answers:

Ok lets start the answer:-

First,

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

T=2π/√(GM/R³)

86400=2π/√(GM/R³)

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!

Regards,

Amresh