If the radius of earth's orbit is made 1/4, the duration of an year will become

Options

A. `(365xx8)` days
B. `(365xx4)` days
C. `((365)/(4))` days
D. `((365)/(8))` days

Answer

D

Explanation

`(T_(1)^(2))/(T_(2)^(2))=(R_(1)^(3))/(((R_(1))/(4))^(3))=(64)/(1)=4^(3)`
`therefore (T_(1))/(T_(2))=(4^(3//2))=8 " " therefore " " T_(2)=(T_(1))/(8)=((365)/(8))` days