If 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. 12 h
B. 6h
C. 4h
D. 2h

Answer

B

Explanation

Conservation angular momentum of the earth wrt its axis of rotation
`I_(1)omega_(1)=I_(2)omega_(2)`
`2/5, MR_(1)^(2), omega_(f)=2/5 M.(R_(1)^(2))/4 omega_(2)`
`rArr omega_(2)=4 omega_(1)` , `T_(1)=(2pi)/(omega_(1)), T_(2)=(2pi)/(omega_(2))`
`(T_(2))/(T_(1))=(omega_(1))/(omega_(2))=1/4, T_(2)=(T_(1))/4=24/4= 6hrs.`