If the earth is one-fourth of its present distance from the sun, the duration of the year will be changed to

Options

A. a) half of the present year
B. b)`(1)/(4)`th of the present year
C. `c)(1)/(8)`th of the present year
D. `d)(7)/(8)`th of the present year

Answer

C

Explanation

From Kepler.s law,
`T^2 prop r^3`
Hence, `((T_1)/(T_2))^2 = ((r_1)/( r_2))^3 = ((r)/( r//4))^3` `(T_1)/( T_2) = (4 )^(3//2)`
`T_2 = (T_1)/( 4^(3//2) )`
`T_2 = (T_1)/( B)`