Abuse SUID bit to run malicious code



I was reading up on the SUID bit just there and something came to
mind.

On my own laptop, let's say I create a simple script something like:

rm /sbin/ifconfig

I then get a USB stick and format it with ext2 and I copy the script
across to the USB stick. Then I do:

sudo chown root:root /mnt/usbstick/my_script
sudo chmod 777 /mnt/usbstick/my_script
such chmod u+s,g+s /mnt/usbstick/my_script

Let's say I bring this USB stick to a computer lab. I mount the USB
stick on a workstation computer. Will I be able to run the script? If
not, why?

(I'm presuming that the script won't run. The only reason I think it
won't run is that it took me only a few seconds to come up with this
idea, and I figure the implementors of Linux are smarter than that,
but still I'd like to know the exact reason why it won't run)

I'd try this out myself for kicks but I haven't got a second computer
to play with.
.