If the mass of the earth remains constant but the duration of the day reduces from 24 hours to 6 hours, then the relation between its new and original radii ( `R_(2)` and (`R_(1)` ) is given by

Options

A. `R_(2)=2R_(1)`
B. `R_(2)=(R_(1))/(2)`
C. `R_(2)=(R_(1))/(3)`
D. `R_(2)=3R_(1)`

Answer

B

Explanation

`I_(1)omega_(1)=I_(2)omega_(2)" "therefore" "MR_(1)^(2)((2pi)/(T_(1)))=MR_(2)^(2)((2pi)/(T_(2)))`
`therefore" "(R_(1)^(2))/(R_(2)^(2))=(T_(1))/(T_(2))=(24)/(6)=(4)/(1)`
`therefore" "(R_(1))/(R_(2))=2" "therefore" "R_(2)=(R_(1))/(2)`