Hide or disable? In this example and in general
I have the following set of controls.

Scenario 1:
If you select one of the first three radio buttons and press Enter, the focus moves to the Passport Number text box. If the user selects "Other", the text field "Other, please specify" enabled and for convenience the screen focus (cursor moves) into this text field.
Scenario 2:
The "Specify Other" text box is hidden until the user clicks the "More Radios" button. By doing so, the text box becomes visible and the cursor is placed in that text box.
Which scenario do you think is the best approach? Perhaps you have another option? Please provide your arguments.
I would also appreciate it if you could make a generalized statement that hiding is better than disabling or vice versa, but I am also interested in this particular example.
Thanks.
Afetrthought: Perhaps in the second example, the text "Please Specify" appears only after the user has selected the "Other" radio button.

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The only time I protect a UI element is when it enhances the UI. If it's just “different” and not “noticeably better,” don't do it.
Users can be sidelined by the fact that the "other" option appears to require you to specify something, but the user interface does not provide any indication that you can do this.
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I would consider number 2 ... Hiding the text box will make it easier for most people to look at the page (each horizontal line creates a barrier to the eye). When someone chooses "other", the text box may disappear with the words "specify" in the box. The form will respond to user input.
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