The world-writable directory that should be placed on a separate partition in order to prevent users from being able to fill up the / filesystem is /tmp. This directory is used by applications and users to store temporary files, and it is world-writable by default. By creating a separate partition for /tmp, the amount ofspace available to users is limited, and the root filesystem is protected from being filled up by temporary files1.

To create a separate partition for /tmp, you can use the fdisk or parted command to create a new partition on the disk. Once the partition is created, you can format it with a filesystem such as ext4, and then mount it to the /tmp directory using the mount command. Finally, you can modify the /etc/fstab file to ensure that the partition is mounted automatically at boot time1. Here is an example of the steps to create a separate partition for /tmp:

After completing these steps, the /tmp directory will be mounted on a separate partition, and users will be limited in the amount of space they can use for temporary files.

References:

LFCS: Linux World-Writable Directory Partitioning