If the earth were to suddenly contract to half of its present radius (without any external torque on it), by what duration would the day be decreased ? Assume earth to be perfect solid sphere of radius `(2)/(5)MR^(2)`.

Options

A. 8 hours
B. 6 hours
C. 4 hours
D. 2 hours

Answer

B

Explanation

Initial moment of inertia, `I=(2)/(5)MR^(2)
New moment of inertia of earth
`I.=(2)/(5)M((R)/(2))^(2)`
`=(1)/(10)MR^(2)`
As external torque is zero `tau=0`
L=constant
`I_(1)omega_(1)=I_(2)omega_(2)`
`I((2pi)/(24))=I.omega_(2)`
`(2)/(5)MR^(2)((2pi)/(24))=(1)/(10)MR^(2)((2pi)/(T))`
T=6 hours