if earth were suddenly shrink to half of its present radius without change in mass,what is the effect on duration of days?

When radius of the earth becomes half of the present radius, Angular momentum of the earth remains same to conserve the angular momentum.
Initial angular momentum = final Angular momentum

$$\begin{gathered} \mathrm{I\omega } = {\mathrm{I}}^{\text{'}}{\mathrm{\omega }}^{\text{'}} \\ \mathrm{where} \mathrm{I} \mathrm{is} \mathrm{the} \mathrm{moment} \mathrm{of} \mathrm{inertia} \mathrm{of} \mathrm{the} \mathrm{earth} \mathrm{at} \mathrm{the} \mathrm{present} \mathrm{radius} \mathrm{R} \\ \mathrm{\omega } \mathrm{is} \mathrm{the} \mathrm{angular} \mathrm{frequency} \mathrm{of} \mathrm{rotation} \mathrm{at} \mathrm{the} \mathrm{pre}s\mathrm{ent} \mathrm{radius} \mathrm{R}. \\ {\mathrm{I}}^{\text{'}} \mathrm{is} \mathrm{the} \mathrm{moment} \mathrm{of} \mathrm{the} \mathrm{inertia} \mathrm{and} {\mathrm{\omega }}^{\text{'} }\mathrm{is} \mathrm{the} \mathrm{angular} \mathrm{frequency} \mathrm{when} \mathrm{radius} \mathrm{becomes} \mathrm{half}. \\ \mathrm{When} \mathrm{mass} \mathrm{of} \mathrm{the} \mathrm{earth} \mathrm{is} \mathrm{constant} , \mathrm{moment} \mathrm{of} \mathrm{inertia} \mathrm{is} \mathrm{directly} \mathrm{proportional} \mathrm{to} \mathrm{the} {\mathrm{R}}^2. \\ \mathrm{\omega } = \frac{2\mathrm{\pi }}{\mathrm{T}} \mathrm{where} \mathrm{T} \mathrm{is} \mathrm{the} \mathrm{timer} \mathrm{period} \mathrm{of} \mathrm{the} \mathrm{earth} \mathrm{which} \mathrm{is} \mathrm{equal} \mathrm{to} 24 \mathrm{hours}. \\ \mathrm{Let} {\mathrm{T}}^{\text{'}} \mathrm{be} \mathrm{the} \mathrm{time} \mathrm{period} \mathrm{of} \mathrm{the} \mathrm{earth} \mathrm{when} \mathrm{radius} \mathrm{becomes} \mathrm{half}. \\ \mathrm{acc}. \mathrm{to} \mathrm{law} \mathrm{of} \mathrm{conservation} \mathrm{of} \mathrm{the} \mathrm{angular} \mathrm{momentum} , \mathrm{we} \mathrm{get} \\ {\mathrm{R}}^2\frac{2\mathrm{\pi }}{\mathrm{T}} = {\left({\mathrm{R}}^{\text{'}}\right)}^2\frac{2\mathrm{\pi }}{{\mathrm{T}}^{\text{'}}} \\ {\mathrm{R}}^{\text{'}} = \mathrm{R}/2 \\ \mathrm{we} \mathrm{get}, \\ {\mathrm{T}}^{\text{'}} = \frac{\mathrm{T}}{4} \\ {\mathrm{T}}^{\text{'}} = 24/4 = 6 \mathrm{hours}. \end{gathered}$$

Hence new duration of the earth is 6 hours.