The question is:
A door is hinged at one end and is free to rotate about a vertical axis. Does its weight cause any torque about this axis? Give reason for your answer.
I think that the answer would be that the weight does produce a torque, since the position vector of each particle and its corresponding weight give the same sense of torque and hence the respective multiplied magnitudes are added up.
If my answer is correct, then there must be a counter-moment which prevents a door from rotating downwards and coming in contact with the floor. Which force produces this torque? I think that the answer might be in the fact that the the axis chosen and the screws attached to the door are distinct. The forces due to these screws must provide the counter-moment.
Are the answers true or need some tinkering/improvement?