I couldn't replicate your error, so I put your script together with anonimonk's script---both work for me. 
#!/usr/bin/perl

use strict;
use warnings;
use FileHandle;

my $log = '/root/Desktop/log.txt';

my $fh1  = FileHandle->new("> $log") or die $!;
print $fh1 "this is a test\n";
$fh1->close;

my $fh2 = FileHandle->new(">> $log") or die $!;
if (defined $fh2) {
    print $fh2 "bar";
    $fh2->close;
}

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In reply to Re: error using FileHandle Module by Khen1950fx
in thread error using FileHandle Module by doubledecker

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