Question

if earth was to suddenly shrink to 1/2 of its present radius without change in mass what will be the duration of day

Answer 1

as the mass is constant gravity will also be same and the duration of fay will be same

Answer 2

Using conservation of angular momentum, 
Moment of inertia is inversely proportional to angular velocity.
Since moment of inertia decreases by 1/4, angular velocity will increase by 1/4.
We know that, time period is inversely proportional to angular velocity hence it will decrease by 1/4 and will be equal to 24/4= 6 hours