how can i delete, clear, or erase the search topics from the pull-down
google search bar?

In Internet Explorer : click "Tools", select "Internet
Options", click "Content" tab, click "AutoComplete", and uncheck
"Forms". To clear previous searches, push "Clear Forms". You can also
delete search queries one by one: empty the Google Search Field and
double-click on it to see the earlier search queries, and delete
individual searches by moving the mouse cursor (or use Down arrow key)
over one of the search queries and press Delete key on keyboard.

If you have Mozilla Firefox: click "Tools", select "Options", click
"Privacy", click "+" next to "Saved Form Information", and uncheck
"Save information I enter in web page forms and the Search Bar". To
clear previous searches, push "Clear" next to "Saved Form
Information".

Your Google search history can be deleted from the Google Toolbar,
from the Google search box, and from your browser. Instructions for
each of these instances appear below:

To clear your search history from the drop-down text box on the Google Toolbar:

1. Click on the 'Google' logo to access the drop-down menu.
2. Select the 'Clear Search History' option. This will clear all the
previous searches from the drop-down box.

If you would like to completely disable your Toolbar's search history,
please click on the 'Options' button directly on your Toolbar and
uncheck the box next to 'Drop-down search history.'

Please note that this only clears the search history from the Google
Toolbar, which is entirely separate from the search history stored by
your browser.

To clear your history from the search box on the Google homepage:

The search history that displays in the search box on the Google
homepage is stored by your browser, not by Google. To disable this
feature on Microsoft Internet Explorer (IE) versions 5.0 and higher:

1. Go to the 'Tools' menu.
2. Select 'Internet Options.'
3. Select the 'Content' tab.
4. Within the 'Personal Information' area, select 'AutoComplete.'
5. Click on 'Clear Forms.' You can also uncheck the 'Forms' box in
this same window to keep this information from being stored in the
future.

Alternatively, you can delete individual entries from your search
history by using the Down arrow key to select a previous search, then
pressing the Delete key once an unwanted search is highlighted.

To clear your history from Internet Explorer:

1. Go to the 'Tools' menu.
2. Select 'Internet Options.'
3. Click the 'General' tab.
4. Click the 'Clear History' button. To completely disable the history
function, set 'Days to keep pages in history' to zero.