This obelisk marks the location Captain Cooks family cottage.
The cottage itself was shipped to Australia for the Centenary of Melbourne in 1934 where is still stands in Fitzroy Park. The cottage was built by Cooks parents in 1755 so its unlikely Cook himself actually lived there as he moved away to Staithes in 1745.
The obelisk is constructed with stone from near Point Hicks which was the first part of Australia spotted by Lieutenant Hicks from the Endeavour. It is a replica of an obelisk that stands there.
The unveiling of the obelisk was actually captured and is available on the Pathe Website.