Variable as module name?

Cody Fendant has asked for the wisdom of the Perl Monks concerning the following question:

I want to do this:

use Foo;
my $object = Foo->new();
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Only I want to replace 'Foo' with a variable determined by some other factor.

my $module_name = 'Foo';
use $module_name;
my $object = $module_name->new();
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I got as far as understanding that use will never be happy with this, is that right? And I ought to use require instead?

My code doesn't give an error if I do this:

$module = 'Foo';
my $module_path = $module . '.pm';
require $module_path;
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But it complains that I'm calling "new" on an unblessed reference when I do my $object = $module->new(); on the next line.