If the radius of the earth contracts to half of its present value without change in its mass, what will be the new duration of the day?

Options

A. 6h
B. 12 h
C. 36 h
D. 144 h

Explanation

In this case we can use conservation of angular momentum to calculate new angular speed.
`I_(1)omega_(1)=I_(2)omega_(2)`
`implies((2)/(5)mr^(2))omega_(1)=[(2)/(5)m((r)/(2))^(2)]omega_(2)`
`implies(omega_(1))/(omega_(2))=(1)/(4)`
`T=2pi//omega` hence time period is inversely proportional to the angular speed.
`(T_(2))/(T_(1))=(omega_(1))/(omega_(2))impliesT_(2)=((omega_(1))/(omega_(2)))T_(1)`
`impliesT_(2)=((1)/(4))(24)=6h`
Hence option (a) is correct.