If the distance between the Earth and Sun were to be doubled from its present value, the number of days in a year would be

Options

A. 64.5
B. 1032
C. 182.5
D. 730

Answer

B

Explanation

`(T_(1)^(2))/(T_(2)^(2))=(r_(1)^(3))/(r_(2)^(3))`
`therefore((T_1)/(T_2))^(2)=((r_1)/(r_2))^(3)`
`r_(1)=r,r_(2)=2r,T_(1)=365"days"`
`therefore((365)/(T_2))^(2)=((r)/(2r))^(3)`
`((365)^2)/((T_(2))^(2))=(1)/(8)`
`thereforeT_(2)^(2)=8xx(365)^(2)`
`T_(2)=2sqrt(2)xx365`
`=2xx1.414xx365`
`1032"days"`