If the polar ice capsmelted, how might this
effect the length of the day?

It will increase the length of the day

Explanation: The polar ice caps contain the solid ice particles found around the polar regions,an increased temperature is a major cause of the melting of the polar ice Caps. When the polar ice caps melt especially in huge volumes they increase the amount of water flowing into the Sea this will cause a rise in the volume of the sea.

This rise in sea level will add some weights to Earth, making the Earth to rotate slightly lower than its normal speed,a slower rotation will lead to longer days.

float.

archimedes' principle

denser than water sinks in water.

denser than mercury would sink in it

at right angles to each other