YOU SAID:

The hat was placed on the head

INTO JAPANESE

帽子は頭にかぶせた

BACK INTO ENGLISH

the hat was put on the head

INTO JAPANESE

帽子を頭にかぶった

BACK INTO ENGLISH

put a hat on one's head

INTO JAPANESE

頭に帽子をかぶる

BACK INTO ENGLISH

put a hat on one's head