Bu şekilde dener misin?
exec('wget http://bilmemne.com/video/ '.$video.'.mp4');
Veya
exec("wget http://bilmemne.com/video/ {$video}.mp4");
exec('wget http://bilmemne.com/video/ '.$video.'.mp4');
exec("wget http://bilmemne.com/video/ {$video}.mp4");