If the radius of earth's orbit is made one-fourth, the duration of a Year will become

According to Kepler's third law of planetary motion
$\begin{array}{l}{\mathrm{T}}^2\propto {\mathrm{R}}^3\\ \therefore \frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}=\frac{{\left({\mathrm{R}}_1\right)}^{3/2}}{{\left({\mathrm{R}}_1/4\right)}^{3/2}}=(4{)}^{3/2}=8\\ \text{ or }{\mathrm{T}}_2={\mathrm{T}}_1/8=\frac{1}{8}\text{ times }\end{array}$